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3 years ago

11

What is the simplest form of the expression representing this quotient?

1 answer:

Tpy6a [65]3 years ago

8 0

9514 1404 393

Answer:

(x +5)/(6x -30)

Step-by-step explanation:

In general, you factor the expressions and cancel factors that can be cancelled. The "invert and multiply" rule for dividing fractions also applies to rational expressions.

$\dfrac{x^2-2x}{x^2-10x+25}\div\dfrac{6x^2-12x}{x^2-25}=\dfrac{x^2-2x}{x^2-10x+25}\times\dfrac{x^2-25}{6x^2-12x}\\\\=\dfrac{x(x-2)(x-5)(x+5)}{6x(x-2)(x-5)(x-5)}=\dfrac{x+5}{6(x-5)}=\boxed{\dfrac{x+5}{6x-30}}\qquad x\notin\{-5,0,2,5\}$

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