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Q. 104

Expert-verifiedFound in: Page 668

Book edition
OER 2017

Author(s)
OPENSTAX

Pages
1346 pages

ISBN
9780998625720

In the following exercises, (a) find the LCD for the given rational expressions (b) rewrite them as equivalent rational expressions with the lowest common denominator.

$\frac{5}{{c}^{2}-4c+4},\frac{3c}{{c}^{2}-7c+10}$

(a) The LCD is $(c-2)(c-2)(c-5)$.

(b) The expressions with LCD are $\frac{5(c-5)}{(c-2)(c-2)(c-5)},\frac{3c}{(c-2)(c-2)(c-5)}$.

The given expressions are $\frac{5}{{c}^{2}-4c+4},\frac{3c}{{c}^{2}-7c+10}$.

- Factor the denominators of both the given rational expressions.

${c}^{2}-4c+4=(c-2)(c-2)\phantom{\rule{0ex}{0ex}}{c}^{2}-7c+10=(c-2)(c-5)$

- So, the LCD is $(c-2)(c-2)(c-5)$.

The given expressions are $\frac{5}{{c}^{2}-4c+4},\frac{3c}{{c}^{2}-7c+10}$

- Multiply and divide the expressions by the missing factor to make the denominator equal to LCD.

$\frac{5}{{c}^{2}-4c+4}=\frac{5(c-5)}{(c-2)(c-2)(c-5)}\phantom{\rule{0ex}{0ex}}\frac{3c}{{c}^{2}-7c+10}=\frac{3c}{(c-2)(c-2)(c-5)}$

- So, the expressions with equal denominators are $\frac{5(c-5)}{(c-2)(c-2)(c-5)},\frac{3c}{(c-2)(c-2)(c-5)}$.

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