Solve M/M-2*M-2*(M-2/2)^-1

$$\frac { M } { M - 2 } \cdot M - 2 \cdot ( \frac { M - 2 } { 2 } ) ^ { - 1 }$$

Evaluate

$$M+2$$

Short Solution Steps

Express \frac{M}{M-2}M as a single fraction.

$$\frac{MM}{M-2}-2\times \left(\frac{M-2}{2}\right)^{-1}$$

To raise \frac{M-2}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{MM}{M-2}-2\times \frac{\left(M-2\right)^{-1}}{2^{-1}}$$

Express 2\times \frac{\left(M-2\right)^{-1}}{2^{-1}} as a single fraction.

$$\frac{MM}{M-2}-\frac{2\left(M-2\right)^{-1}}{2^{-1}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{MM}{M-2}-2^{2}\times \frac{1}{M-2}$$

Multiply M and M to get M^{2}.

$$\frac{M^{2}}{M-2}-2^{2}\times \frac{1}{M-2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{M^{2}}{M-2}-4\times \frac{1}{M-2}$$

Express 4\times \frac{1}{M-2} as a single fraction.

$$\frac{M^{2}}{M-2}-\frac{4}{M-2}$$

Since \frac{M^{2}}{M-2} and \frac{4}{M-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{M^{2}-4}{M-2}$$

Factor the expressions that are not already factored in \frac{M^{2}-4}{M-2}.

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

Cancel out M-2 in both numerator and denominator.

$$M+2$$

Expand

$$M+2$$

Short Solution Steps

Express \frac{M}{M-2}M as a single fraction.

$$\frac{MM}{M-2}-2\times \left(\frac{M-2}{2}\right)^{-1}$$

To raise \frac{M-2}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{MM}{M-2}-2\times \frac{\left(M-2\right)^{-1}}{2^{-1}}$$

Express 2\times \frac{\left(M-2\right)^{-1}}{2^{-1}} as a single fraction.

$$\frac{MM}{M-2}-\frac{2\left(M-2\right)^{-1}}{2^{-1}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{MM}{M-2}-2^{2}\times \frac{1}{M-2}$$

Multiply M and M to get M^{2}.

$$\frac{M^{2}}{M-2}-2^{2}\times \frac{1}{M-2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{M^{2}}{M-2}-4\times \frac{1}{M-2}$$

Express 4\times \frac{1}{M-2} as a single fraction.

$$\frac{M^{2}}{M-2}-\frac{4}{M-2}$$

Since \frac{M^{2}}{M-2} and \frac{4}{M-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{M^{2}-4}{M-2}$$

Factor the expressions that are not already factored in \frac{M^{2}-4}{M-2}.

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

Cancel out M-2 in both numerator and denominator.

$$M+2$$