Question

Simplify$\frac{7\mathrm{y}-35}{25-{\mathrm{y}}^2}$

Short answer

Simplified expression is$\frac{-7}{5+\mathrm{y}}.$

Step-by-step solution

Step 1. Given Data

Given that the expression is$\frac{7\mathrm{y}-35}{25-{\mathrm{y}}^2}.$

Step 2. Simplification

On factorize and applying the square difference,

$$\begin{gathered} =\frac{7\mathrm{y}-35}{5^2-{\mathrm{y}}^2} \\ =\frac{7(\mathrm{y}-5)}{(5-\mathrm{y})(5+\mathrm{y})} \\ =\frac{-7(\mathrm{y}-5)}{(\mathrm{y}-5)(5+\mathrm{y})} \\ =\frac{\mathbf{-}\mathbf{7}}{\mathbf{5}\mathbf{+}\mathbf{y}} \end{gathered}$$