Question: Simplify. \frac{4x^2 - 32x}{5x^2 - 40x}

Solution

To simplify the given expression \[ \frac{4x^2 - 32x}{5x^2 - 40x} \] first, factor both the numerator and the denominator. The numerator is \(4x^2 - 32x\). Factor out the greatest common factor, which is \(4x\): \[ 4x(x - 8) \] The denominator is \(5x^2 - 40x\). Factor out the greatest common factor, which is \(5x\): \[ 5x(x - 8) \] Now, the expression is \[ \frac{4x(x - 8)}{5x(x - 8)} \] Cancel the common factor \((x - 8)\): \[ \frac{4x}{5x} \] Now, simplify the fraction by cancelling \(x\): \[ \frac{4}{5} \] So, the simplified expression is \[ \frac{4}{5} \]