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2023-02-19

Multiplying $\frac{3}{17-2}$ by which fraction will produce an equivalent fraction with a rational denominator.

Rigoberto Gordon

$=\frac{3}{17-2}×\left(\frac{17+2}{17+2}\right)=\frac{3\left(17+2\right)}{{\left(17\right)}^{2}-{\left(2\right)}^{2}}\left(\because \left(a-b\right)\left(a+b\right)={a}^{2}-{b}^{2}\right)=\frac{3\left(17+2\right)}{17-2}=\frac{3\left(17+2\right)}{15}=\frac{\left(17+2\right)}{5}$We have to multiply $\frac{17+2}{17+2}$ to the given expression to get a rational denominator.