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Question

# Acid or subtract. $\frac { 6 r s } { r ^ { 2 } s ^ { 2 } } + \frac { 18 r } { r ^ { 2 } s ^ { 2 } }$

Solution

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Step 1
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To add the following rational expression, we must make sure the denominators are the same.

$\dfrac{6rs}{r^2s^2}+ \dfrac{18r}{r^2s^2}$

Add the numerators, put that result over the denominator.

$\dfrac{6rs+18r}{r^2s^2}$

Simplify the fraction by taking $6r$ as a common factor

$\dfrac{6r(s+3)}{r^2s^2}$

Remove $r$ by using quotient rule which state $\color{#4257b2}\dfrac{a^m}{a^n}=a^{m-n}$

$\therefore\ \dfrac{6rs}{r^2s^2}+ \dfrac{18r}{r^2s^2}=\dfrac{6(s+3)}{rs^2}$

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