$\frac{ax-b}{x-c}$* $\frac{c-x}{ax+b}$
You asked:
Evaluate the expression: \(\frac{a x - b}{x - c} \cdot \frac{c - x}{a x + b}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{a x - b}{x - c} \cdot \frac{c - x}{a x + b} = \frac{\left(c - x\right) \left(a x - b\right)}{\left(- c + x\right) \left(a x + b\right)} \)
Expanded
\[\frac{a x - b}{x - c} \cdot \frac{c - x}{a x + b} = \frac{a c x}{- a c x + x^{2} a - b c + b x} - \frac{x^{2} a}{- a c x + x^{2} a - b c + b x} - \frac{b c}{- a c x + x^{2} a - b c + b x} + \frac{b x}{- a c x + x^{2} a - b c + b x}\]
Factored
\[\frac{a x - b}{x - c} \cdot \frac{c - x}{a x + b} = - \frac{a x - b}{a x + b}\]