Question

quiz: rational expressions
hs: algebra 2b m (sequential) / 4:ra

1. multiply

\\(\frac{y^2 - 2y}{y^2 + 7y - 18} \cdot \frac{y^2 - 81}{y^2 - 11y + 18}\\)
options:
\\(\frac{y}{(y - 2)(y - 9)}\\)
\\(\frac{y + 9}{y - 2}\\)
\\(\frac{y}{y - 2}\\)
\\(\frac{y}{y + 2}\\)

Explanation:

Step1: Factor all polynomials

Numerator 1: $y^2-2y = y(y-2)$
Denominator 1: $y^2+7y-18=(y+9)(y-2)$
Numerator 2: $y^2-81=(y+9)(y-9)$
Denominator 2: $y^2-11y+18=(y-2)(y-9)$

Step2: Write product of factored forms

$\frac{y(y-2)}{(y+9)(y-2)} \cdot \frac{(y+9)(y-9)}{(y-2)(y-9)}$

Step3: Cancel common factors

Cancel $y-2$, $y+9$, $y-9$: $\frac{y}{y-2}$

Answer:

$\frac{y}{y-2}$