Question

Please explain, but not to wordy​

Answer 1

Solving the expression $\frac{x^2-12x+32}{x^2-10x+16}.\frac{6x-30}{25-5x}$ we get $-\frac{6(x-4)}{5(x-2)}$

Step-by-step explanation:

Solving the expression:

$\frac{x^2-12x+32}{x^2-10x+16}.\frac{6x-30}{25-5x}$

Solving the expression:

We will find factors of the quadratic terms:

$x^2-12x+32\\=x^2-8x-4x+32\\=x(x-8)-4(x-8)\\=(x-4)(x-8)$

So, factors of $x^2-12x+32$ are $(x-4)(x-8)$

$x^2-10x+16\\=x^2-8x-2x+16\\=x(x-8)-2(x-8)\\=(x-2)(x-8)$

So, factors of $x^2-10x+16$ are $(x-2)(x-8)$

Placing factors instead of quadratic equation and finding common terms:

$\frac{(x-4)(x-8)}{(x-2)(x-8)}.\frac{6(x-5)}{-5(x-5)}$

Cancelling the common terms:

$\frac{(x-4)}{(x-2)}.\frac{6}{-5}\\-\frac{6(x-4)}{5(x-2)}$

So, Solving the expression $\frac{x^2-12x+32}{x^2-10x+16}.\frac{6x-30}{25-5x}$ we get $-\frac{6(x-4)}{5(x-2)}$

Keywords: Solving Fractions

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