Question

For z ≠ 0, which of the following expressions is equivalent to -50z^2 + 35z/-45z^2 + 40z?

Answer 1

To simplify the expression \(-\frac{50z^2 + 35z}{-45z^2 + 40z}\), we can begin by factoring both the numerator and the denominator.

**Step 1: Factor out common terms**

1. In the numerator:
\[
-50z^2 + 35z = -5z(10z - 7)
\]

2. In the denominator:
\[
-45z^2 + 40z = -5z(9z - 8)
\]

**Step 2: Substitute factored forms back into the expression**

Now, we can rewrite the original expression:
\[
-\frac{-5z(10z - 7)}{-5z(9z - 8)}
\]

**Step 3: Cancel common factors**

Since \(z \neq 0\), we can safely cancel \(-5z\) from both the numerator and the denominator:
\[
\frac{10z - 7}{9z - 8}
\]

Thus, the expression \(-\frac{50z^2 + 35z}{-45z^2 + 40z}\) simplifies to:
\[
\frac{10z - 7}{9z - 8}
\]

This indicates that the equivalent expression is:
\[
\frac{10z - 7}{9z - 8}
\]