Solve wy-wv+8xy-8xv/y^2-v^2*4y+4v+wy+vw/16-w^2

$$\frac { w y - w v + 8 x y - 8 x v } { y ^ { 2 } - v ^ { 2 } } \cdot \frac { 4 y + 4 v + w y + v w } { 16 - w ^ { 2 } }$$

Evaluate

$$-\frac{8x+w}{w-4}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{wy-wv+8xy-8xv}{y^{2}-v^{2}}.

$$\frac{\left(8x+w\right)\left(y-v\right)}{\left(y+v\right)\left(y-v\right)}\times \frac{4y+4v+wy+vw}{16-w^{2}}$$

Cancel out y-v in both numerator and denominator.

$$\frac{8x+w}{y+v}\times \frac{4y+4v+wy+vw}{16-w^{2}}$$

Factor the expressions that are not already factored in \frac{4y+4v+wy+vw}{16-w^{2}}.

$$\frac{8x+w}{y+v}\times \frac{\left(w+4\right)\left(y+v\right)}{\left(w-4\right)\left(-w-4\right)}$$

Extract the negative sign in 4+w.

$$\frac{8x+w}{y+v}\times \frac{-\left(-w-4\right)\left(y+v\right)}{\left(w-4\right)\left(-w-4\right)}$$

Cancel out -w-4 in both numerator and denominator.

$$\frac{8x+w}{y+v}\times \frac{-\left(y+v\right)}{w-4}$$

Multiply \frac{8x+w}{y+v} times \frac{-\left(y+v\right)}{w-4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(8x+w\right)\left(-1\right)\left(y+v\right)}{\left(y+v\right)\left(w-4\right)}$$

Cancel out y+v in both numerator and denominator.

$$\frac{-\left(8x+w\right)}{w-4}$$

To find the opposite of 8x+w, find the opposite of each term.

$$\frac{-8x-w}{w-4}$$

Expand

$$\frac{8x+w}{4-w}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{wy-wv+8xy-8xv}{y^{2}-v^{2}}.

$$\frac{\left(8x+w\right)\left(y-v\right)}{\left(y+v\right)\left(y-v\right)}\times \frac{4y+4v+wy+vw}{16-w^{2}}$$

Cancel out y-v in both numerator and denominator.

$$\frac{8x+w}{y+v}\times \frac{4y+4v+wy+vw}{16-w^{2}}$$

Factor the expressions that are not already factored in \frac{4y+4v+wy+vw}{16-w^{2}}.

$$\frac{8x+w}{y+v}\times \frac{\left(w+4\right)\left(y+v\right)}{\left(w-4\right)\left(-w-4\right)}$$

Extract the negative sign in 4+w.

$$\frac{8x+w}{y+v}\times \frac{-\left(-w-4\right)\left(y+v\right)}{\left(w-4\right)\left(-w-4\right)}$$

Cancel out -w-4 in both numerator and denominator.

$$\frac{8x+w}{y+v}\times \frac{-\left(y+v\right)}{w-4}$$

Multiply \frac{8x+w}{y+v} times \frac{-\left(y+v\right)}{w-4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(8x+w\right)\left(-1\right)\left(y+v\right)}{\left(y+v\right)\left(w-4\right)}$$

Cancel out y+v in both numerator and denominator.

$$\frac{-\left(8x+w\right)}{w-4}$$

To find the opposite of 8x+w, find the opposite of each term.

$$\frac{-8x-w}{w-4}$$