Simplification Or Other Simple Results - Tiger Algebra

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Enter an equation or problemClear Solve × Camera input is not recognized!axy/|abs|( )789*456-%123+<>0,.=abcabcdefghijklmnopqrstuvwxyz␣.Solution - Simplification or other simple results (3x+4)/(x+7) (3x+4)/(x+7)

Other Ways to Solve

Simplification or other simple results

Step by Step Solution

Step 1 :

Equation at the end of step 1 :

Step 2 :

Equation at the end of step 2 :

Step 3 :

9x2 - 16 Simplify —————————————— 3x2 + 17x - 28

Trying to factor as a Difference of Squares :

3.1 Factoring: 9x2 - 16 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 : 9 is the square of 3 Check : 16 is the square of 4Check : x2 is the square of x1 Factorization is : (3x + 4) • (3x - 4)

Trying to factor by splitting the middle term

3.2 Factoring 3x2 + 17x - 28 The first term is, 3x2 its coefficient is 3 .The middle term is, +17x its coefficient is 17 .The last term, "the constant", is -28 Step-1 : Multiply the coefficient of the first term by the constant 3 • -28 = -84 Step-2 : Find two factors of -84 whose sum equals the coefficient of the middle term, which is 17 .

-84	+	1	=	-83
-42	+	2	=	-40
-28	+	3	=	-25
-21	+	4	=	-17
-14	+	6	=	-8
-12	+	7	=	-5
-7	+	12	=	5
-6	+	14	=	8
-4	+	21	=	17	That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 21 3x2 - 4x + 21x - 28Step-4 : Add up the first 2 terms, pulling out like factors : x • (3x-4) Add up the last 2 terms, pulling out common factors : 7 • (3x-4) Step-5 : Add up the four terms of step 4 : (x+7) • (3x-4) Which is the desired factorization

Canceling Out :

3.3 Cancel out (3x-4) which appears on both sides of the fraction line.

Final result :

3x + 4 —————— x + 7

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Terms and topics

• Canceling out

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