Pergunta

Simplify. (frac (2)/(uv^2))((1)/(v)+(3)/(u^2))
Solução

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MarcusElite · Tutor por 8 anos
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To simplify the given expression, we can follow these steps:<br /><br />1. Find a common denominator for the terms in the denominator of the fraction.<br />2. Simplify the fraction by multiplying the numerator and denominator by the common denominator.<br />3. Cancel out any common factors between the numerator and denominator.<br /><br />Let's start with step 1:<br /><br />$\frac {1}{v}+\frac {3}{u^{2}} = \frac {u^{2}}{vu^{2}}+\frac {3v}{vu^{2}} = \frac {u^{2}+3v}{vu^{2}}$<br /><br />Now, we can move on to step 2:<br /><br />$\frac {\frac {2}{uv^{2}}}{\frac {u^{2}+3v}{vu^{2}}} = \frac {2}{uv^{2}} \cdot \frac {vu^{2}}{u^{2}+3v} = \frac {2vu^{2}}{uv^{2}(u^{2}+3v)}$<br /><br />Finally, we can simplify the expression by canceling out the common factors:<br /><br />$\frac {2vu^{2}}{uv^{2}(u^{2}+3v)} = \frac {2u}{u^{2}+3v}$<br /><br />Therefore, the simplified expression is $\frac {2u}{u^{2}+3v}$.
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