Solve 2-x/5x-1{2+frac{4/x}}

$$\frac { 2 - x } { 5 x - \frac { 1 } { 2 + \frac { 4 } { x } } }$$

Evaluate

$$\frac{2\left(4-x^{2}\right)}{x\left(10x+19\right)}$$

Short Solution Steps

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

$$\frac{2-x}{5x-\frac{1}{\frac{2x}{x}+\frac{4}{x}}}$$

Since \frac{2x}{x} and \frac{4}{x} have the same denominator, add them by adding their numerators.

$$\frac{2-x}{5x-\frac{1}{\frac{2x+4}{x}}}$$

Divide 1 by \frac{2x+4}{x} by multiplying 1 by the reciprocal of \frac{2x+4}{x}.

$$\frac{2-x}{5x-\frac{x}{2x+4}}$$

Factor 2x+4.

$$\frac{2-x}{5x-\frac{x}{2\left(x+2\right)}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5x times \frac{2\left(x+2\right)}{2\left(x+2\right)}.

$$\frac{2-x}{\frac{5x\times 2\left(x+2\right)}{2\left(x+2\right)}-\frac{x}{2\left(x+2\right)}}$$

Since \frac{5x\times 2\left(x+2\right)}{2\left(x+2\right)} and \frac{x}{2\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-x}{\frac{5x\times 2\left(x+2\right)-x}{2\left(x+2\right)}}$$

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

$$\frac{2-x}{\frac{10x^{2}+20x-x}{2\left(x+2\right)}}$$

Combine like terms in 10x^{2}+20x-x.

$$\frac{2-x}{\frac{10x^{2}+19x}{2\left(x+2\right)}}$$

Divide 2-x by \frac{10x^{2}+19x}{2\left(x+2\right)} by multiplying 2-x by the reciprocal of \frac{10x^{2}+19x}{2\left(x+2\right)}.

$$\frac{\left(2-x\right)\times 2\left(x+2\right)}{10x^{2}+19x}$$

Use the distributive property to multiply 2-x by 2.

$$\frac{\left(4-2x\right)\left(x+2\right)}{10x^{2}+19x}$$

Apply the distributive property by multiplying each term of 4-2x by each term of x+2.

$$\frac{4x+8-2x^{2}-4x}{10x^{2}+19x}$$

Combine 4x and -4x to get 0.

$$\frac{8-2x^{2}}{10x^{2}+19x}$$

Expand

$$-\frac{2\left(x^{2}-4\right)}{10x^{2}+19x}$$

Short Solution Steps

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

$$\frac{2-x}{5x-\frac{1}{\frac{2x}{x}+\frac{4}{x}}}$$

Since \frac{2x}{x} and \frac{4}{x} have the same denominator, add them by adding their numerators.

$$\frac{2-x}{5x-\frac{1}{\frac{2x+4}{x}}}$$

Divide 1 by \frac{2x+4}{x} by multiplying 1 by the reciprocal of \frac{2x+4}{x}.

$$\frac{2-x}{5x-\frac{x}{2x+4}}$$

Factor 2x+4.

$$\frac{2-x}{5x-\frac{x}{2\left(x+2\right)}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5x times \frac{2\left(x+2\right)}{2\left(x+2\right)}.

$$\frac{2-x}{\frac{5x\times 2\left(x+2\right)}{2\left(x+2\right)}-\frac{x}{2\left(x+2\right)}}$$

Since \frac{5x\times 2\left(x+2\right)}{2\left(x+2\right)} and \frac{x}{2\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-x}{\frac{5x\times 2\left(x+2\right)-x}{2\left(x+2\right)}}$$

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

$$\frac{2-x}{\frac{10x^{2}+20x-x}{2\left(x+2\right)}}$$

Combine like terms in 10x^{2}+20x-x.

$$\frac{2-x}{\frac{10x^{2}+19x}{2\left(x+2\right)}}$$

Divide 2-x by \frac{10x^{2}+19x}{2\left(x+2\right)} by multiplying 2-x by the reciprocal of \frac{10x^{2}+19x}{2\left(x+2\right)}.

$$\frac{\left(2-x\right)\times 2\left(x+2\right)}{10x^{2}+19x}$$

Use the distributive property to multiply 2-x by 2.

$$\frac{\left(4-2x\right)\left(x+2\right)}{10x^{2}+19x}$$

Apply the distributive property by multiplying each term of 4-2x by each term of x+2.

$$\frac{4x+8-2x^{2}-4x}{10x^{2}+19x}$$

Combine 4x and -4x to get 0.

$$\frac{8-2x^{2}}{10x^{2}+19x}$$