Simplify the right side of the equation. f(x)=x^{2}+12x+35/ x^{2}-3x-40

Jessie Lee

Jessie Lee

Answered question

2021-12-07

Simplify the right side of the equation.
f(x)=x2+12x+35x23x40

Answer & Explanation

intacte87

intacte87

Beginner2021-12-08Added 42 answers

Step 1
We have to simplify the right side of equation:
f(x)=x2+12x+35x23x40
We need to factorize the numerator and denominator by middle term splitting method,
so factorizing the numerator
since 35=7×5
and 12=7+5
Therefore,
x2+12x+35=x2+7x+5x+35
=x(x+7)+5(x+7)
=(x+7)(x+5)
Hence, factorization of numerator is (x+7)(x+5).
Now factorizing the denominator,
since, 40=8×5 and -8+5=-3
Therefore,
x23x40=x28x+5x40
=x(x-8)+5(x-8)
=(x-8)(x+5)
Hence, factorization of denominator is (x-8)(x+5).
Step 2
Putting above values in the equation, we get
f(x)=x2+12x+35x23x40
=(x+7)(x+5)(x8)(x+5)
=x+7x8
Hence, after simplification of right side of equation is f(x)=x+7x8.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?