## Intermediate Algebra: Connecting Concepts through Application

The expression for the missing side $= 10x-3$.
Let $y =$ the expression for the missing side $(4x-7)y = 40x^{2}-82x+21$ $y = \frac{40x^{2}-82x+21}{4x-7}$ $= \frac{40x^{2}-70x-12x+21}{4x-7}$ $= \frac{10x(4x-7)-3(4x-7)}{4x-7}$ $= \frac{(10x-3)(4x-7)}{4x-7}$ $= \frac{(10x-3)}{1}$ $y = 10x-3$