Solve (m-1)^2/4+4m^3:1-m^2/(2m+2)^2=

$$\frac { ( m - 1 ) ^ { 2 } } { 4 + 4 m ^ { 3 } } : \frac { 1 - m ^ { 2 } } { ( 2 m + 2 ) ^ { 2 } } =$$

Evaluate

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

Short Solution Steps

Divide \frac{\left(m-1\right)^{2}}{4+4m^{3}} by \frac{1-m^{2}}{\left(2m+2\right)^{2}} by multiplying \frac{\left(m-1\right)^{2}}{4+4m^{3}} by the reciprocal of \frac{1-m^{2}}{\left(2m+2\right)^{2}}.

$$\frac{\left(m-1\right)^{2}\left(2m+2\right)^{2}}{\left(4+4m^{3}\right)\left(1-m^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(m-1\right)^{2}\left(2m+2\right)^{2}}{4\left(m-1\right)\left(-m-1\right)\left(m+1\right)\left(m^{2}-m+1\right)}$$

Cancel out m-1 in both numerator and denominator.

$$\frac{\left(m-1\right)\left(2m+2\right)^{2}}{4\left(-m-1\right)\left(m+1\right)\left(m^{2}-m+1\right)}$$

Expand the expression.

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

Factor the expressions that are not already factored.

$$\frac{4\left(m-1\right)\left(m+1\right)^{2}}{4\left(-m-1\right)\left(m+1\right)\left(m^{2}-m+1\right)}$$

Cancel out 4\left(m+1\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{m^{2}-1}{-m^{3}-1}$$

Factor the expressions that are not already factored.

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

Cancel out m+1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

Divide \frac{\left(m-1\right)^{2}}{4+4m^{3}} by \frac{1-m^{2}}{\left(2m+2\right)^{2}} by multiplying \frac{\left(m-1\right)^{2}}{4+4m^{3}} by the reciprocal of \frac{1-m^{2}}{\left(2m+2\right)^{2}}.

$$\frac{\left(m-1\right)^{2}\left(2m+2\right)^{2}}{\left(4+4m^{3}\right)\left(1-m^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(m-1\right)^{2}\left(2m+2\right)^{2}}{4\left(m-1\right)\left(-m-1\right)\left(m+1\right)\left(m^{2}-m+1\right)}$$

Cancel out m-1 in both numerator and denominator.

$$\frac{\left(m-1\right)\left(2m+2\right)^{2}}{4\left(-m-1\right)\left(m+1\right)\left(m^{2}-m+1\right)}$$

Expand the expression.

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

Factor the expressions that are not already factored.

$$\frac{4\left(m-1\right)\left(m+1\right)^{2}}{4\left(-m-1\right)\left(m+1\right)\left(m^{2}-m+1\right)}$$

Cancel out 4\left(m+1\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{m^{2}-1}{-m^{3}-1}$$

Factor the expressions that are not already factored.

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

Cancel out m+1 in both numerator and denominator.

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