Question

Rewrite as equivalent rational expressions with denominator (5c+9)(c−3)(c−8): 8/5c2−6c−27,2c/5c2−31c−72

Answer 1

Rational expressions are expressions that can be represented as a quotient

The equivalent rational expression of $\mathbf{\frac{(5c + 9)(c - 3)}{c - 8}}$ is $\mathbf{\frac{5c^2 -6c-27}{c - 8}}$

The expression is given as:

$\mathbf{\frac{(5c + 9)(c - 3)}{c - 8}}$

Expand the numerator as follows

$\mathbf{\frac{(5c + 9)(c - 3)}{c - 8} = \frac{(5c \times c -5c \times 3 + 9\times c -9 \times 3)}{c - 8}}$

Multiply the factors on the numerator

$\mathbf{\frac{(5c + 9)(c - 3)}{c - 8} = \frac{(5c^2 -15c+ 9c -27)}{c - 8}}$

Collect and evaluate like terms

$\mathbf{\frac{(5c + 9)(c - 3)}{c - 8} = \frac{(5c^2 -6c-27)}{c - 8}}$

Remove the brackets

$\mathbf{\frac{(5c + 9)(c - 3)}{c - 8} = \frac{5c^2 -6c-27}{c - 8}}$

This means that:

$\mathbf{\frac{5c^2 -6c-27}{c - 8}}$ and the given expression $\mathbf{\frac{(5c + 9)(c - 3)}{c - 8}}$ are equivalent

Hence, the equivalent rational expression of $\mathbf{\frac{(5c + 9)(c - 3)}{c - 8}}$ is $\mathbf{\frac{5c^2 -6c-27}{c - 8}}$

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https://brainly.com/question/25292194