Solve x-[y/1+(frac{1{1+y/2})}]

$$x - [ \frac { y } { 1 + ( \frac { 1 } { 1 + y / 2 } ) } ]$$

Evaluate

$$\frac{xy+4x-y^{2}-2y}{y+4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

$$x-\frac{y}{1+\frac{1}{\frac{2}{2}+\frac{y}{2}}}$$

Since \frac{2}{2} and \frac{y}{2} have the same denominator, add them by adding their numerators.

$$x-\frac{y}{1+\frac{1}{\frac{2+y}{2}}}$$

Divide 1 by \frac{2+y}{2} by multiplying 1 by the reciprocal of \frac{2+y}{2}.

$$x-\frac{y}{1+\frac{2}{2+y}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2+y}{2+y}.

$$x-\frac{y}{\frac{2+y}{2+y}+\frac{2}{2+y}}$$

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

$$x-\frac{y}{\frac{2+y+2}{2+y}}$$

Combine like terms in 2+y+2.

$$x-\frac{y}{\frac{4+y}{2+y}}$$

Divide y by \frac{4+y}{2+y} by multiplying y by the reciprocal of \frac{4+y}{2+y}.

$$x-\frac{y\left(2+y\right)}{4+y}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{4+y}{4+y}.

$$\frac{x\left(4+y\right)}{4+y}-\frac{y\left(2+y\right)}{4+y}$$

Since \frac{x\left(4+y\right)}{4+y} and \frac{y\left(2+y\right)}{4+y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\left(4+y\right)-y\left(2+y\right)}{4+y}$$

Do the multiplications in x\left(4+y\right)-y\left(2+y\right).

$$\frac{4x+xy-2y-y^{2}}{4+y}$$

Differentiate w.r.t. x

$$1$$