Question

Express the following difference in the simplest form $?$

$\frac{8}{5\mathrm{d}+4}-\frac{1}{2\mathrm{d}-3}$

Answer 1

Find the difference in the simplest form:

$$\begin{gathered} \frac{8}{5\mathrm{d}+4}-\frac{1}{2\mathrm{d}-3}=\frac{8(2\mathrm{d}-3)-1(5\mathrm{d}+4)}{(5\mathrm{d}+4)(2\mathrm{d}-3)}\left[\mathrm{simplify}\mathrm{by}\mathrm{taking}\mathrm{the}\mathrm{least}\mathrm{common}\mathrm{denominator}\right] \\ =\frac{16\mathrm{d}-24-5\mathrm{d}-4}{(5\mathrm{d}+4)(2\mathrm{d}-3)}\left[\mathrm{group}\mathrm{the}\mathrm{like}\mathrm{terms}\mathrm{together}\right] \end{gathered}$$

$=\frac{(16\mathrm{d}-5\mathrm{d})+(-24-4)}{(5\mathrm{d}+4)(2\mathrm{d}-3)}\left[\mathrm{combine}\mathrm{the}\mathrm{like}\mathrm{term}\mathrm{together}\right]$

$=\frac{11\mathrm{d}-28}{(5\mathrm{d}+4)(2\mathrm{d}-3)}$

Hence, the difference in the simplest form is $\frac{\mathbf{11}\mathbf{d}\mathbf{-}\mathbf{28}}{\mathbf{(}\mathbf{5}\mathbf{d}\mathbf{+}\mathbf{4}\mathbf{)}\mathbf{(}\mathbf{2}\mathbf{d}\mathbf{-}\mathbf{3}\mathbf{)}}$.