Question

Simplify$\frac{9(8-2)-3(15-7)}{6(7-1)-3(17-9)}$

Short answer

On simplifying the given expression, we get

$\frac{9(8-2)-3(15-7)}{6(7-1)-3(17-9)}=\frac{5}{2}$

Step-by-step solution

Step 1. Given information

The given expression is

$\frac{9(8-2)-3(15-7)}{6(7-1)-3(17-9)}$

We have to simplify the given expression.

Step 2. Simplify the numerator and denominator 

$\begin{array}{l}\Rightarrow \frac{9(8-2)-3(15-7)}{6(7-1)-3(17-9)}=\frac{9\left(6\right)-3\left(8\right)}{6\left(6\right)-3\left(8\right)}\\ =\frac{54-24}{36-24}\\ =\frac{30}{12}\end{array}$

Step 3. Simplify the fraction 

$\begin{array}{l}\Rightarrow \frac{9(8-2)-3(15-7)}{6(7-1)-3(17-9)}=\frac{30}{12}\\ =\frac{\cancel{6}\times 5}{\cancel{6}\times 2}\\ =\frac{5}{2}\end{array}$