Question
simplify \( \frac{4}{m-\left(m-\frac{4}{m^{2}-1}\right)} \)
Ask by Barnett Wade. in Malaysia
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( m^{2} - 1 \)
Solution
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:**
\[
m^{2} - 1
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To simplify the expression \( \frac{4}{m - \left( m - \frac{4}{m^2 - 1} \right)} \), first simplify the inner parentheses: \[ m - \left( m - \frac{4}{m^2 - 1} \right) = m - m + \frac{4}{m^2 - 1} = \frac{4}{m^2 - 1} \] Now substitute this back into the original expression: \[ \frac{4}{\frac{4}{m^2 - 1}} \] To simplify this further, multiply by the reciprocal: \[ \frac{4 \cdot (m^2 - 1)}{4} = m^2 - 1 \] So, the simplified expression is: \[ m^2 - 1 \]
