Question

Simplify$\frac{8(9-2)-4(14-9)}{7(8-3)-3(16-9)}$

Short answer

On simplifying the given expression, we get

$\frac{8(9-2)-4(14-9)}{7(8-3)-3(16-9)}=\frac{18}{7}$

Step-by-step solution

Step 1. Given information 

The given expression is

$\frac{8(9-2)-4(14-9)}{7(8-3)-3(16-9)}$

We have to simplify the given expression.

Step 2. Simplify the numerator and denominator 

Now,

$\begin{array}{l}\Rightarrow \frac{8(9-2)-4(14-9)}{7(8-3)-3(16-9)}=\frac{8\left(7\right)-4\left(5\right)}{7\left(5\right)-3\left(7\right)}\\ =\frac{56-20}{35-21}\\ =\frac{36}{14}\end{array}$

Step 3. Simplify the fraction 

$\begin{array}{l}\Rightarrow \frac{8(9-2)-4(14-9)}{7(8-3)-3(16-9)}=\frac{36}{14}\\ =\frac{\cancel{2}\times 18}{\cancel{2}\times 7}\\ =\frac{18}{7}\end{array}$