Question

Simplify the expression if possible. $$\frac{12-5 x}{10 x^{2}-24 x}$$

Short answer

The simplified expression is \(\frac{-1}{2x}\).

Step-by-step solution

Factorize the Numerator and Denominator

Start by examining both the numerator and denominator for any common factors. The numerator \(12 - 5x\) can be written as \(12 - 5x\), which has no other common factor. However, the denominator \(10x^2 - 24x\) has a common factor of \(2x\). So it can be written as \(2x(5x - 12)\). Now your expression looks like this: \(\frac{12 - 5x}{2x(5x - 12)}\).

Rearrange the Numerator

To simplify the expression further, rearrange the numerator as \(-5x + 12\), which can be written as \(-1*(5x - 12)\). Now, your expression looks like this: \(\frac{-1*(5x - 12)}{2x(5x - 12)}\).

Cancel Out Common Terms

Since both the numerator and denominator now have the same term \((5x - 12)\), these can be canceled out, leaving us with \(\frac{-1}{2x}\).