Solve Addingsubtractingfindingleastcommonmultiple H/4-1/h-3 Tiger ...

Step 1 :

1 Simplify — h

Equation at the end of step 1 :

h 1 (— - —) - 3 4 h

Step 2 :

h Simplify — 4

Equation at the end of step 2 :

h 1 (— - —) - 3 4 h

Step 3 :

Calculating the Least Common Multiple :

3.1 Find the Least Common Multiple The left denominator is : 4 The right denominator is : h

Number of times each prime factor appears in the factorization of:

Prime Factor	Left Denominator	Right Denominator	L.C.M = Max {Left,Right}
2	2	0	2
Product of all Prime Factors	4	1	4

Number of times each Algebraic Factor appears in the factorization of:

Algebraic Factor	Left Denominator	Right Denominator	L.C.M = Max {Left,Right}
h	0	1	1

Least Common Multiple: 4h

Calculating Multipliers :

3.2 Calculate multipliers for the two fractions Denote the Least Common Multiple by L.C.M Denote the Left Multiplier by Left_M Denote the Right Multiplier by Right_M Denote the Left Deniminator by L_Deno Denote the Right Multiplier by R_Deno Left_M = L.C.M / L_Deno = h Right_M = L.C.M / R_Deno = 4

Making Equivalent Fractions :

3.3 Rewrite the two fractions into equivalent fractionsTwo fractions are called equivalent if they have the same numeric value. For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well. To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. h • h —————————————————— = ————— L.C.M 4h R. Mult. • R. Num. 4 —————————————————— = —— L.C.M 4h

Adding fractions that have a common denominator :

3.4 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:

h • h - (4) h2 - 4 ——————————— = —————— 4h 4h

Equation at the end of step 3 :

(h2 - 4) ———————— - 3 4h

Step 4 :

Rewriting the whole as an Equivalent Fraction :

4.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using 4h as the denominator :

3 3 • 4h 3 = — = —————— 1 4h

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

Trying to factor as a Difference of Squares :

4.2 Factoring: h2 - 4 Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)Proof : (A+B) • (A-B) = A2 - AB + BA - B2 = A2 - AB + AB - B2 = A2 - B2Note : AB = BA is the commutative property of multiplication. Note : - AB + AB equals zero and is therefore eliminated from the expression.Check : 4 is the square of 2Check : h2 is the square of h1 Factorization is : (h + 2) • (h - 2)

Adding fractions that have a common denominator :

4.3 Adding up the two equivalent fractions

(h+2) • (h-2) - (3 • 4h) h2 - 12h - 4 ———————————————————————— = ———————————— 4h 4h

Trying to factor by splitting the middle term

4.4 Factoring h2 - 12h - 4 The first term is, h2 its coefficient is 1 .The middle term is, -12h its coefficient is -12 .The last term, "the constant", is -4 Step-1 : Multiply the coefficient of the first term by the constant 1 • -4 = -4 Step-2 : Find two factors of -4 whose sum equals the coefficient of the middle term, which is -12 .

-4	+	1	=	-3
-2	+	2	=	0
-1	+	4	=	3

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

Final result :

h2 - 12h - 4 ———————————— 4h