Solving the expression [tex]\frac{x^2-12x+32}{x^2-10x+16}.\frac{6x-30}{25-5x}[/tex] we get [tex]-\frac{6(x-4)}{5(x-2)}[/tex]
Step-by-step explanation:
Solving the expression:
[tex]\frac{x^2-12x+32}{x^2-10x+16}.\frac{6x-30}{25-5x}[/tex]
Solving the expression:
We will find factors of the quadratic terms:
[tex]x^2-12x+32\\=x^2-8x-4x+32\\=x(x-8)-4(x-8)\\=(x-4)(x-8)[/tex]
So, factors of [tex]x^2-12x+32[/tex] are [tex](x-4)(x-8)[/tex]
[tex]x^2-10x+16\\=x^2-8x-2x+16\\=x(x-8)-2(x-8)\\=(x-2)(x-8)[/tex]
So, factors of [tex]x^2-10x+16[/tex] are [tex](x-2)(x-8)[/tex]
Placing factors instead of quadratic equation and finding common terms:
[tex]\frac{(x-4)(x-8)}{(x-2)(x-8)}.\frac{6(x-5)}{-5(x-5)}[/tex]
Cancelling the common terms:
[tex]\frac{(x-4)}{(x-2)}.\frac{6}{-5}\\-\frac{6(x-4)}{5(x-2)}[/tex]
So, Solving the expression [tex]\frac{x^2-12x+32}{x^2-10x+16}.\frac{6x-30}{25-5x}[/tex] we get [tex]-\frac{6(x-4)}{5(x-2)}[/tex]
Keywords: Solving Fractions
Learn more about Solving Fractions at:
- brainly.com/question/2456302
- brainly.com/question/4390083
- brainly.com/question/2456302
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