Question

Subtract$\frac{4y+3}{2y-1}-5$

Short answer

The simplification of the rational expression is$\frac{-6y+8}{2y-1}$.

Step-by-step solution

Given information 

The given rational expression is$\frac{4y+3}{2y-1}-5$

The simplification of the rational expression 

Write 5 as $\frac{5}{1}$to have 5 rational expressions .

The LCD of $2y-1\mathrm{and}1\mathrm{is}\left(2\mathrm{y}-1\right)$.

Rewrite $\frac{5}{1}$as an equivalent rational expressions with the LCD.

$\frac{4y+3}{2y-1}-\frac{5\left(2y-1\right)}{1\left(2y-1\right)}$

Simplify

$$\begin{gathered} =\frac{4y+3}{2y-1}-\frac{5\left(2y-1\right)}{1\left(2y-1\right)} \\ Simplify \\ =\frac{4y+3}{2y-1}-\frac{10y-5}{2y-1} \\ =\frac{4y+3-10y+5}{2y-1} \\ =\frac{-6y+8}{2y-1} \\ \mathrm{Factor}\mathrm{common}\mathrm{factors} \\ \frac{-6\mathrm{y}+8}{2\mathrm{y}-1} \end{gathered}$$