Question

\left(4-2x\right)\left(\frac{-6x^2+10x+21}{4-2x}\right)

Answer 1

To simplify the expression \(\left(4-2x\right)\left(\frac{-6x^2+10x+21}{4-2x}\right)\), we can cancel out the common factor \((4-2x)\) from the numerator and the denominator, as long as \(4-2x \neq 0\):

1. Identify the factor that can be canceled:
\[
4 - 2x \neq 0 \Rightarrow x \neq 2
\]

2. Cancel the common factor:
\[
\left(4-2x\right) \left(\frac{-6x^2+10x+21}{4-2x}\right) = -6x^2 + 10x + 21 \quad \text{(for \(x \neq 2\))}
\]

Thus, the simplified expression is:
\[
-6x^2 + 10x + 21 \quad \text{(for \(4 - 2x \neq 0\))}
\]