Simplify \(\frac{2}{a+b}-\frac{1}{a-b}\)
Question 1 Report
Simplify \(\frac{2}{a+b}-\frac{1}{a-b}\)
Answer Details
To simplify the expression, we need to find a common denominator for the two fractions.
We can use the difference of two squares identity \((a+b)(a-b) = a^2-b^2\) to find a common denominator.
\begin{aligned} \frac{2}{a+b}-\frac{1}{a-b} &= \frac{2(a-b)}{(a+b)(a-b)} - \frac{1(a+b)}{(a-b)(a+b)}\\ &= \frac{2(a-b)-1(a+b)}{a^2-b^2}\\ &= \frac{2a-2b-a-b}{a^2-b^2}\\ &= \frac{a-3b}{a^2-b^2} \end{aligned}
Therefore, the simplified expression is \(\frac{a-3b}{a^2-b^2}\), which corresponds to.
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