Question

Simplify the following expression:6m^2 -60m/ m^2 -2m -80 / m-7/ 8m- 56
The simplest form is

Answer 1

To simplify the expression \(\frac{6m^2 - 60m}{m^2 - 2m - 80} \div \frac{m - 7}{8m - 56}\), we start by rewriting the division as multiplication by the reciprocal:

\[
\frac{6m^2 - 60m}{m^2 - 2m - 80} \times \frac{8m - 56}{m - 7}
\]

Now, let's simplify each part of the expression step by step.

1. **Factor \(6m^2 - 60m\):**

\[
6m^2 - 60m = 6m(m - 10)
\]

2. **Factor \(m^2 - 2m - 80\):**

To factor \(m^2 - 2m - 80\), we look for two numbers that multiply to \(-80\) and add to \(-2\). These numbers are \(8\) and \(-10\):

\[
m^2 - 2m - 80 = (m - 10)(m + 8)
\]

3. **Factor \(8m - 56\):**

\[
8m - 56 = 8(m - 7)
\]

Now, we can rewrite the expression with its factored forms:

\[
\frac{6m(m - 10)}{(m - 10)(m + 8)} \times \frac{8(m - 7)}{m - 7}
\]

Next, we can cancel out \(m - 10\) from the numerator and the denominator and \(m - 7\) from the numerator and the denominator:

\[
\frac{6m \cancel{(m - 10)}}{\cancel{(m - 10)}(m + 8)} \times \frac{8\cancel{(m - 7)}}{\cancel{(m - 7)}}
\]

This simplifies to:

\[
\frac{6m \cdot 8}{m + 8} = \frac{48m}{m + 8}
\]

Thus, the simplest form of the expression is:

\[
\frac{48m}{m + 8}
\]