Solve (m + n)/(m - n) - (m - n)/(m + n) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{m+n}{m-n}-\frac{m-n}{m+n}$$

Evaluate

$\frac{4mn}{m^{2}-n^{2}}$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $m-n$ and $m+n$ is $\left(m+n\right)\left(m-n\right)$. Multiply $\frac{m+n}{m-n}$ times $\frac{m+n}{m+n}$. Multiply $\frac{m-n}{m+n}$ times $\frac{m-n}{m-n}$.

$$\frac{\left(m+n\right)\left(m+n\right)}{\left(m+n\right)\left(m-n\right)}-\frac{\left(m-n\right)\left(m-n\right)}{\left(m+n\right)\left(m-n\right)}$$

Since $\frac{\left(m+n\right)\left(m+n\right)}{\left(m+n\right)\left(m-n\right)}$ and $\frac{\left(m-n\right)\left(m-n\right)}{\left(m+n\right)\left(m-n\right)}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(m+n\right)\left(m+n\right)-\left(m-n\right)\left(m-n\right)}{\left(m+n\right)\left(m-n\right)}$$

Do the multiplications in $\left(m+n\right)\left(m+n\right)-\left(m-n\right)\left(m-n\right)$.

$$\frac{m^{2}+mn+mn+n^{2}-m^{2}+mn+mn-n^{2}}{\left(m+n\right)\left(m-n\right)}$$

Combine like terms in $m^{2}+mn+mn+n^{2}-m^{2}+mn+mn-n^{2}$.

$$\frac{4mn}{\left(m+n\right)\left(m-n\right)}$$

Expand $\left(m+n\right)\left(m-n\right)$.

$$\frac{4mn}{m^{2}-n^{2}}$$

Expand

$\frac{4mn}{m^{2}-n^{2}}$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $m-n$ and $m+n$ is $\left(m+n\right)\left(m-n\right)$. Multiply $\frac{m+n}{m-n}$ times $\frac{m+n}{m+n}$. Multiply $\frac{m-n}{m+n}$ times $\frac{m-n}{m-n}$.

$$\frac{\left(m+n\right)\left(m+n\right)}{\left(m+n\right)\left(m-n\right)}-\frac{\left(m-n\right)\left(m-n\right)}{\left(m+n\right)\left(m-n\right)}$$

Since $\frac{\left(m+n\right)\left(m+n\right)}{\left(m+n\right)\left(m-n\right)}$ and $\frac{\left(m-n\right)\left(m-n\right)}{\left(m+n\right)\left(m-n\right)}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(m+n\right)\left(m+n\right)-\left(m-n\right)\left(m-n\right)}{\left(m+n\right)\left(m-n\right)}$$

Do the multiplications in $\left(m+n\right)\left(m+n\right)-\left(m-n\right)\left(m-n\right)$.

$$\frac{m^{2}+mn+mn+n^{2}-m^{2}+mn+mn-n^{2}}{\left(m+n\right)\left(m-n\right)}$$

Combine like terms in $m^{2}+mn+mn+n^{2}-m^{2}+mn+mn-n^{2}$.

$$\frac{4mn}{\left(m+n\right)\left(m-n\right)}$$

Expand $\left(m+n\right)\left(m-n\right)$.

$$\frac{4mn}{m^{2}-n^{2}}$$