Perform the multiplication or division and simplify. \frac{x+ 3}{4x^{2}-9}\div\frac{x^{2}+7x+12}{2^{2}+7x-15}

Miracle Graves

Miracle Graves

Answered question

2022-02-15

Perform the multiplication or division and simplify.
x+34x29÷x2+7x+1222+7x15

Answer & Explanation

rossegues03b

rossegues03b

Beginner2022-02-16Added 11 answers

simplify:
x+34x29÷x2+7x+1222+7x15
Inverting and changing to multiplication:
x+34x29÷x2+7x+1222+7x15
=x+34x29×x2+7x+1222+7x15
factorizing the quadratics:
=x+3(2x)232×2x2+10x15x2+4x+12
=x+3(2x3)(2x+3){×2x(x+5)3(x+5)x(x+4)+3(x+4)
=x+3(2x3)(2x+3){×(2x3)(x+5)(x+3)(x+4)
cancelling the same terms, we get:
=x+32x3(2x+3){×2x3(x+5)x+3(x+4)
=(x+5)(2x+3)(x+4){

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