Solve Reducingfractionstolowestterms H2+8h/3h2-9h-4h+6/3h2-9h ...

Reformatting the input :

Changes made to your input should not affect the solution: (1): "h2" was replaced by "h^2". 2 more similar replacement(s).

Step 1 :

2 Simplify — 1

Equation at the end of step 1 :

h (((((h2)+((8•—)•(h2)))-9h)-4h)+(2•h2))-9h 3

Step 2 :

Equation at the end of step 2 :

h (((((h2)+((8•—)•(h2)))-9h)-4h)+2h2)-9h 3

Step 3 :

h Simplify — 3

Equation at the end of step 3 :

h (((((h2)+((8•—)•h2))-9h)-4h)+2h2)-9h 3

Step 4 :

Multiplying exponential expressions :

4.1 h1 multiplied by h2 = h(1 + 2) = h3

Equation at the end of step 4 :

8h3 (((((h2)+———)-9h)-4h)+2h2)-9h 3

Step 5 :

Rewriting the whole as an Equivalent Fraction :

5.1 Adding a fraction to a whole Rewrite the whole as a fraction using 3 as the denominator :

h2 h2 • 3 h2 = —— = —————— 1 3

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

5.2 Adding up the two equivalent fractions Add the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

h2 • 3 + 8h3 8h3 + 3h2 ———————————— = ————————— 3 3

Equation at the end of step 5 :

(8h3 + 3h2) (((——————————— - 9h) - 4h) + 2h2) - 9h 3

Step 6 :

Rewriting the whole as an Equivalent Fraction :

6.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using 3 as the denominator :

9h 9h • 3 9h = —— = —————— 1 3

Step 7 :

Pulling out like terms :

7.1 Pull out like factors : 8h3 + 3h2 = h2 • (8h + 3)

Adding fractions that have a common denominator :

7.2 Adding up the two equivalent fractions

h2 • (8h+3) - (9h • 3) 8h3 + 3h2 - 27h —————————————————————— = ——————————————— 3 3

Equation at the end of step 7 :

(8h3 + 3h2 - 27h) ((————————————————— - 4h) + 2h2) - 9h 3

Step 8 :

Rewriting the whole as an Equivalent Fraction :

8.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using 3 as the denominator :

4h 4h • 3 4h = —— = —————— 1 3

Step 9 :

Pulling out like terms :

9.1 Pull out like factors : 8h3 + 3h2 - 27h = h • (8h2 + 3h - 27)

Trying to factor by splitting the middle term

9.2 Factoring 8h2 + 3h - 27 The first term is, 8h2 its coefficient is 8 .The middle term is, +3h its coefficient is 3 .The last term, "the constant", is -27 Step-1 : Multiply the coefficient of the first term by the constant 8 • -27 = -216 Step-2 : Find two factors of -216 whose sum equals the coefficient of the middle term, which is 3 .

-216	+	1	=	-215
-108	+	2	=	-106
-72	+	3	=	-69
-54	+	4	=	-50
-36	+	6	=	-30
-27	+	8	=	-19
-24	+	9	=	-15
-18	+	12	=	-6
-12	+	18	=	6
-9	+	24	=	15
-8	+	27	=	19
-6	+	36	=	30
-4	+	54	=	50
-3	+	72	=	69
-2	+	108	=	106
-1	+	216	=	215

Observation : No two such factors can be found !! Conclusion : Trinomial can not be factored

Adding fractions that have a common denominator :

9.3 Adding up the two equivalent fractions

h • (8h2+3h-27) - (4h • 3) 8h3 + 3h2 - 39h —————————————————————————— = ——————————————— 3 3

Equation at the end of step 9 :

(8h3 + 3h2 - 39h) (————————————————— + 2h2) - 9h 3

Step 10 :

Rewriting the whole as an Equivalent Fraction :

10.1 Adding a whole to a fraction Rewrite the whole as a fraction using 3 as the denominator :

2h2 2h2 • 3 2h2 = ——— = ——————— 1 3

Step 11 :

Pulling out like terms :

11.1 Pull out like factors : 8h3 + 3h2 - 39h = h • (8h2 + 3h - 39)

Trying to factor by splitting the middle term

11.2 Factoring 8h2 + 3h - 39 The first term is, 8h2 its coefficient is 8 .The middle term is, +3h its coefficient is 3 .The last term, "the constant", is -39 Step-1 : Multiply the coefficient of the first term by the constant 8 • -39 = -312 Step-2 : Find two factors of -312 whose sum equals the coefficient of the middle term, which is 3 .

-312	+	1	=	-311
-156	+	2	=	-154
-104	+	3	=	-101
-78	+	4	=	-74
-52	+	6	=	-46
-39	+	8	=	-31
-26	+	12	=	-14
-24	+	13	=	-11
-13	+	24	=	11
-12	+	26	=	14
-8	+	39	=	31
-6	+	52	=	46
-4	+	78	=	74
-3	+	104	=	101
-2	+	156	=	154
-1	+	312	=	311

Observation : No two such factors can be found !! Conclusion : Trinomial can not be factored

Adding fractions that have a common denominator :

11.3 Adding up the two equivalent fractions

h • (8h2+3h-39) + 2h2 • 3 8h3 + 9h2 - 39h ————————————————————————— = ——————————————— 3 3

Equation at the end of step 11 :

(8h3 + 9h2 - 39h) ————————————————— - 9h 3

Step 12 :

Rewriting the whole as an Equivalent Fraction :

12.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using 3 as the denominator :

9h 9h • 3 9h = —— = —————— 1 3

Step 13 :

Pulling out like terms :

13.1 Pull out like factors : 8h3 + 9h2 - 39h = h • (8h2 + 9h - 39)

Trying to factor by splitting the middle term

13.2 Factoring 8h2 + 9h - 39 The first term is, 8h2 its coefficient is 8 .The middle term is, +9h its coefficient is 9 .The last term, "the constant", is -39 Step-1 : Multiply the coefficient of the first term by the constant 8 • -39 = -312 Step-2 : Find two factors of -312 whose sum equals the coefficient of the middle term, which is 9 .

-312	+	1	=	-311
-156	+	2	=	-154
-104	+	3	=	-101
-78	+	4	=	-74
-52	+	6	=	-46
-39	+	8	=	-31
-26	+	12	=	-14
-24	+	13	=	-11
-13	+	24	=	11
-12	+	26	=	14
-8	+	39	=	31
-6	+	52	=	46
-4	+	78	=	74
-3	+	104	=	101
-2	+	156	=	154
-1	+	312	=	311

Observation : No two such factors can be found !! Conclusion : Trinomial can not be factored

Adding fractions that have a common denominator :

13.3 Adding up the two equivalent fractions

h • (8h2+9h-39) - (9h • 3) 8h3 + 9h2 - 66h —————————————————————————— = ——————————————— 3 3

Step 14 :

Pulling out like terms :

14.1 Pull out like factors : 8h3 + 9h2 - 66h = h • (8h2 + 9h - 66)

Trying to factor by splitting the middle term

14.2 Factoring 8h2 + 9h - 66 The first term is, 8h2 its coefficient is 8 .The middle term is, +9h its coefficient is 9 .The last term, "the constant", is -66 Step-1 : Multiply the coefficient of the first term by the constant 8 • -66 = -528 Step-2 : Find two factors of -528 whose sum equals the coefficient of the middle term, which is 9 .

-528	+	1	=	-527
-264	+	2	=	-262
-176	+	3	=	-173
-132	+	4	=	-128
-88	+	6	=	-82
-66	+	8	=	-58

For tidiness, printing of 14 lines which failed to find two such factors, was suppressedObservation : No two such factors can be found !! Conclusion : Trinomial can not be factored

Final result :

h • (8h2 + 9h + 66) ——————————————————— 3