Divide as indicated. Simplify the answer. (x^(2)+12x+35)/(x^(2)+4x-21)-:(x^(2)+2x-15)/(4x-12)

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asked Jul 18, 2024 198k views

2 votes

Divide as indicated. Simplify the answer. (x^(2)+12x+35)/(x^(2)+4x-21)-:(x^(2)+2x-15)/(4x-12)

Mathematics
high-school

Jordanpg asked

by Jordanpg

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1 Answer

4 votes

Answer:

Hi,

Explanation:

$1) x^2+12x+35=x^2+5x+7x+35=x(x+5)+7(x+5)=(x+5)(x+7)\\\\2) x^2+4x-21=x^2+7x-3x-21=x(x+7)-3(x+7)=(x+7)(x-3)\\\\3) x^2+2x-15=x^2+5x-3x-15=x(x+5)-3(x+5)=(x+5)(x-3)\\$

$((x^2+12x+35)/(x^2+4x-21) )/((x^2+2x-15)/(4x-12) ) \\\\=(x^2+12x+35)/(x^2+4x-21)*(4x-12)/(x^2+2x-15)\\ \\=((x+5)(x+7)*4*(x-3))/((x+7)(x-3)(x+5)(x-3)) \\\\\boxed{=(4)/(x-3) }$