Solve 2-3/a-2/4-frac{1{a+2}}

$$\frac { 2 - \frac { 3 } { a - 2 } } { 4 - \frac { 1 } { a + 2 } }$$

Evaluate

$$\frac{\left(2a-7\right)\left(a+2\right)}{\left(a-2\right)\left(4a+7\right)}$$

Short Solution Steps

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

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

Since \frac{2\left(a-2\right)}{a-2} and \frac{3}{a-2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2\left(a-2\right)-3.

$$\frac{\frac{2a-4-3}{a-2}}{4-\frac{1}{a+2}}$$

Combine like terms in 2a-4-3.

$$\frac{\frac{2a-7}{a-2}}{4-\frac{1}{a+2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{a+2}{a+2}.

$$\frac{\frac{2a-7}{a-2}}{\frac{4\left(a+2\right)}{a+2}-\frac{1}{a+2}}$$

Since \frac{4\left(a+2\right)}{a+2} and \frac{1}{a+2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2a-7}{a-2}}{\frac{4\left(a+2\right)-1}{a+2}}$$

Do the multiplications in 4\left(a+2\right)-1.

$$\frac{\frac{2a-7}{a-2}}{\frac{4a+8-1}{a+2}}$$

Combine like terms in 4a+8-1.

$$\frac{\frac{2a-7}{a-2}}{\frac{4a+7}{a+2}}$$

Divide \frac{2a-7}{a-2} by \frac{4a+7}{a+2} by multiplying \frac{2a-7}{a-2} by the reciprocal of \frac{4a+7}{a+2}.

$$\frac{\left(2a-7\right)\left(a+2\right)}{\left(a-2\right)\left(4a+7\right)}$$

Apply the distributive property by multiplying each term of 2a-7 by each term of a+2.

$$\frac{2a^{2}+4a-7a-14}{\left(a-2\right)\left(4a+7\right)}$$

Combine 4a and -7a to get -3a.

$$\frac{2a^{2}-3a-14}{\left(a-2\right)\left(4a+7\right)}$$

Apply the distributive property by multiplying each term of a-2 by each term of 4a+7.

$$\frac{2a^{2}-3a-14}{4a^{2}+7a-8a-14}$$

Combine 7a and -8a to get -a.

$$\frac{2a^{2}-3a-14}{4a^{2}-a-14}$$

Expand

$$\frac{2a^{2}-3a-14}{\left(a-2\right)\left(4a+7\right)}$$

Short Solution Steps

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

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

Since \frac{2\left(a-2\right)}{a-2} and \frac{3}{a-2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2\left(a-2\right)-3.

$$\frac{\frac{2a-4-3}{a-2}}{4-\frac{1}{a+2}}$$

Combine like terms in 2a-4-3.

$$\frac{\frac{2a-7}{a-2}}{4-\frac{1}{a+2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{a+2}{a+2}.

$$\frac{\frac{2a-7}{a-2}}{\frac{4\left(a+2\right)}{a+2}-\frac{1}{a+2}}$$

Since \frac{4\left(a+2\right)}{a+2} and \frac{1}{a+2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2a-7}{a-2}}{\frac{4\left(a+2\right)-1}{a+2}}$$

Do the multiplications in 4\left(a+2\right)-1.

$$\frac{\frac{2a-7}{a-2}}{\frac{4a+8-1}{a+2}}$$

Combine like terms in 4a+8-1.

$$\frac{\frac{2a-7}{a-2}}{\frac{4a+7}{a+2}}$$

Divide \frac{2a-7}{a-2} by \frac{4a+7}{a+2} by multiplying \frac{2a-7}{a-2} by the reciprocal of \frac{4a+7}{a+2}.

$$\frac{\left(2a-7\right)\left(a+2\right)}{\left(a-2\right)\left(4a+7\right)}$$

Apply the distributive property by multiplying each term of 2a-7 by each term of a+2.

$$\frac{2a^{2}+4a-7a-14}{\left(a-2\right)\left(4a+7\right)}$$

Combine 4a and -7a to get -3a.

$$\frac{2a^{2}-3a-14}{\left(a-2\right)\left(4a+7\right)}$$

Apply the distributive property by multiplying each term of a-2 by each term of 4a+7.

$$\frac{2a^{2}-3a-14}{4a^{2}+7a-8a-14}$$

Combine 7a and -8a to get -a.

$$\frac{2a^{2}-3a-14}{4a^{2}-a-14}$$