simplify $$ \frac{4}{m-\left(m-\frac{4}{m^{2}-1}\right)} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{4}{m - \left(m - \frac{4}{m^{2} - 1}\right)}
$$

**Step 1: Simplify the Denominator**

First, simplify the expression inside the denominator:

$$
m - \left(m - \frac{4}{m^{2} - 1}\right) = m - m + \frac{4}{m^{2} - 1} = \frac{4}{m^{2} - 1}
$$

**Step 2: Simplify the Entire Fraction**

Now, substitute the simplified denominator back into the original expression:

$$
\frac{4}{\frac{4}{m^{2} - 1}} = 4 \times \frac{m^{2} - 1}{4} = m^{2} - 1
$$

**Final Answer:**

$$
m^{2} - 1
$$
$$ m^{2} - 1 $$

simplify