Solve (m+2+5/2-m)*2m-4/3-m

$$( m + 2 + \frac { 5 } { 2 - m } ) \cdot \frac { 2 m - 4 } { 3 - m }$$

Evaluate

$$-2m-6$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply m+2 times \frac{2-m}{2-m}.

$$\left(\frac{\left(m+2\right)\left(2-m\right)}{2-m}+\frac{5}{2-m}\right)\times \frac{2m-4}{3-m}$$

Since \frac{\left(m+2\right)\left(2-m\right)}{2-m} and \frac{5}{2-m} have the same denominator, add them by adding their numerators.

$$\frac{\left(m+2\right)\left(2-m\right)+5}{2-m}\times \frac{2m-4}{3-m}$$

Do the multiplications in \left(m+2\right)\left(2-m\right)+5.

$$\frac{2m-m^{2}+4-2m+5}{2-m}\times \frac{2m-4}{3-m}$$

Combine like terms in 2m-m^{2}+4-2m+5.

$$\frac{-m^{2}+9}{2-m}\times \frac{2m-4}{3-m}$$

Multiply \frac{-m^{2}+9}{2-m} times \frac{2m-4}{3-m} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(-m^{2}+9\right)\left(2m-4\right)}{\left(2-m\right)\left(3-m\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\left(m-3\right)\left(m-2\right)\left(-m-3\right)}{\left(-m+2\right)\left(-m+3\right)}$$

Extract the negative sign in -3+m. Extract the negative sign in -2+m.

$$\frac{-\left(-1\right)\times 2\left(-m-3\right)\left(-m+2\right)\left(-m+3\right)}{\left(-m+2\right)\left(-m+3\right)}$$

Cancel out \left(-m+2\right)\left(-m+3\right) in both numerator and denominator.

$$-\left(-1\right)\times 2\left(-m-3\right)$$

Expand the expression.

$$-2m-6$$

Expand

$$-2m-6$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply m+2 times \frac{2-m}{2-m}.

$$\left(\frac{\left(m+2\right)\left(2-m\right)}{2-m}+\frac{5}{2-m}\right)\times \frac{2m-4}{3-m}$$

Since \frac{\left(m+2\right)\left(2-m\right)}{2-m} and \frac{5}{2-m} have the same denominator, add them by adding their numerators.

$$\frac{\left(m+2\right)\left(2-m\right)+5}{2-m}\times \frac{2m-4}{3-m}$$

Do the multiplications in \left(m+2\right)\left(2-m\right)+5.

$$\frac{2m-m^{2}+4-2m+5}{2-m}\times \frac{2m-4}{3-m}$$

Combine like terms in 2m-m^{2}+4-2m+5.

$$\frac{-m^{2}+9}{2-m}\times \frac{2m-4}{3-m}$$

Multiply \frac{-m^{2}+9}{2-m} times \frac{2m-4}{3-m} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(-m^{2}+9\right)\left(2m-4\right)}{\left(2-m\right)\left(3-m\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\left(m-3\right)\left(m-2\right)\left(-m-3\right)}{\left(-m+2\right)\left(-m+3\right)}$$

Extract the negative sign in -3+m. Extract the negative sign in -2+m.

$$\frac{-\left(-1\right)\times 2\left(-m-3\right)\left(-m+2\right)\left(-m+3\right)}{\left(-m+2\right)\left(-m+3\right)}$$

Cancel out \left(-m+2\right)\left(-m+3\right) in both numerator and denominator.

$$-\left(-1\right)\times 2\left(-m-3\right)$$

Expand the expression.

$$-2m-6$$