Solve ((1)/((m)^(2)-m)-(1)/(m-1))\times(m)/(m+2)+(m+1)/(m+2) | 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

$$( \frac{ 1 }{ { m }^{ 2 } -m } - \frac{ 1 }{ m-1 } ) \times \frac{ m }{ m+2 } + \frac{ m+1 }{ m+2 }$$

Evaluate

$\frac{m}{m+2}$

Short Solution Steps

Factor $m^{2}-m$.

$$\left(\frac{1}{m\left(m-1\right)}-\frac{1}{m-1}\right)\times \frac{m}{m+2}+\frac{m+1}{m+2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $m\left(m-1\right)$ and $m-1$ is $m\left(m-1\right)$. Multiply $\frac{1}{m-1}$ times $\frac{m}{m}$.

$$\left(\frac{1}{m\left(m-1\right)}-\frac{m}{m\left(m-1\right)}\right)\times \frac{m}{m+2}+\frac{m+1}{m+2}$$

Since $\frac{1}{m\left(m-1\right)}$ and $\frac{m}{m\left(m-1\right)}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-m}{m\left(m-1\right)}\times \frac{m}{m+2}+\frac{m+1}{m+2}$$

Extract the negative sign in $1-m$.

$$\frac{-\left(m-1\right)}{m\left(m-1\right)}\times \frac{m}{m+2}+\frac{m+1}{m+2}$$

Cancel out $m-1$ in both numerator and denominator.

$$\frac{-1}{m}\times \frac{m}{m+2}+\frac{m+1}{m+2}$$

Multiply $\frac{-1}{m}$ times $\frac{m}{m+2}$ by multiplying numerator times numerator and denominator times denominator.

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

Cancel out $m$ in both numerator and denominator.

$$\frac{-1}{m+2}+\frac{m+1}{m+2}$$

Since $\frac{-1}{m+2}$ and $\frac{m+1}{m+2}$ have the same denominator, add them by adding their numerators.

$$\frac{-1+m+1}{m+2}$$

Combine like terms in $-1+m+1$.

$$\frac{m}{m+2}$$

Expand

$\frac{m}{m+2}$

Short Solution Steps

Factor $m^{2}-m$.

$$\left(\frac{1}{m\left(m-1\right)}-\frac{1}{m-1}\right)\times \frac{m}{m+2}+\frac{m+1}{m+2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $m\left(m-1\right)$ and $m-1$ is $m\left(m-1\right)$. Multiply $\frac{1}{m-1}$ times $\frac{m}{m}$.

$$\left(\frac{1}{m\left(m-1\right)}-\frac{m}{m\left(m-1\right)}\right)\times \frac{m}{m+2}+\frac{m+1}{m+2}$$

Since $\frac{1}{m\left(m-1\right)}$ and $\frac{m}{m\left(m-1\right)}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-m}{m\left(m-1\right)}\times \frac{m}{m+2}+\frac{m+1}{m+2}$$

Extract the negative sign in $1-m$.

$$\frac{-\left(m-1\right)}{m\left(m-1\right)}\times \frac{m}{m+2}+\frac{m+1}{m+2}$$

Cancel out $m-1$ in both numerator and denominator.

$$\frac{-1}{m}\times \frac{m}{m+2}+\frac{m+1}{m+2}$$

Multiply $\frac{-1}{m}$ times $\frac{m}{m+2}$ by multiplying numerator times numerator and denominator times denominator.

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

Cancel out $m$ in both numerator and denominator.

$$\frac{-1}{m+2}+\frac{m+1}{m+2}$$

Since $\frac{-1}{m+2}$ and $\frac{m+1}{m+2}$ have the same denominator, add them by adding their numerators.

$$\frac{-1+m+1}{m+2}$$

Combine like terms in $-1+m+1$.

$$\frac{m}{m+2}$$