Expand the fraction $\frac{2\sin\left(t\right)+5\tan\left(t\right)}{\tan\left(t\right)}$ into $2$ simpler fractions with common denominator $\tan\left(t\right)$

Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

Divide fractions $\frac{2\sin\left(t\right)}{\frac{\sin\left(t\right)}{\cos\left(t\right)}}$ with Keep, Change, Flip: $a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}$

Simplify the fraction $\frac{2\sin\left(t\right)\cos\left(t\right)}{\sin\left(t\right)}$ by $\sin\left(t\right)$