Solve 6+1/x+1/5-frac{3{x-3}}

$$\frac { 6 + \frac { 1 } { x + 1 } } { 5 - \frac { 3 } { x - 3 } }$$

Evaluate

$$\frac{\left(x-3\right)\left(6x+7\right)}{\left(5x-18\right)\left(x+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{x+1}{x+1}.

$$\frac{\frac{6\left(x+1\right)}{x+1}+\frac{1}{x+1}}{5-\frac{3}{x-3}}$$

Since \frac{6\left(x+1\right)}{x+1} and \frac{1}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{6\left(x+1\right)+1}{x+1}}{5-\frac{3}{x-3}}$$

Do the multiplications in 6\left(x+1\right)+1.

$$\frac{\frac{6x+6+1}{x+1}}{5-\frac{3}{x-3}}$$

Combine like terms in 6x+6+1.

$$\frac{\frac{6x+7}{x+1}}{5-\frac{3}{x-3}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{x-3}{x-3}.

$$\frac{\frac{6x+7}{x+1}}{\frac{5\left(x-3\right)}{x-3}-\frac{3}{x-3}}$$

Since \frac{5\left(x-3\right)}{x-3} and \frac{3}{x-3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{6x+7}{x+1}}{\frac{5\left(x-3\right)-3}{x-3}}$$

Do the multiplications in 5\left(x-3\right)-3.

$$\frac{\frac{6x+7}{x+1}}{\frac{5x-15-3}{x-3}}$$

Combine like terms in 5x-15-3.

$$\frac{\frac{6x+7}{x+1}}{\frac{5x-18}{x-3}}$$

Divide \frac{6x+7}{x+1} by \frac{5x-18}{x-3} by multiplying \frac{6x+7}{x+1} by the reciprocal of \frac{5x-18}{x-3}.

$$\frac{\left(6x+7\right)\left(x-3\right)}{\left(x+1\right)\left(5x-18\right)}$$

Apply the distributive property by multiplying each term of 6x+7 by each term of x-3.

$$\frac{6x^{2}-18x+7x-21}{\left(x+1\right)\left(5x-18\right)}$$

Combine -18x and 7x to get -11x.

$$\frac{6x^{2}-11x-21}{\left(x+1\right)\left(5x-18\right)}$$

Apply the distributive property by multiplying each term of x+1 by each term of 5x-18.

$$\frac{6x^{2}-11x-21}{5x^{2}-18x+5x-18}$$

Combine -18x and 5x to get -13x.

$$\frac{6x^{2}-11x-21}{5x^{2}-13x-18}$$

Expand

$$\frac{6x^{2}-11x-21}{\left(5x-18\right)\left(x+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{x+1}{x+1}.

$$\frac{\frac{6\left(x+1\right)}{x+1}+\frac{1}{x+1}}{5-\frac{3}{x-3}}$$

Since \frac{6\left(x+1\right)}{x+1} and \frac{1}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{6\left(x+1\right)+1}{x+1}}{5-\frac{3}{x-3}}$$

Do the multiplications in 6\left(x+1\right)+1.

$$\frac{\frac{6x+6+1}{x+1}}{5-\frac{3}{x-3}}$$

Combine like terms in 6x+6+1.

$$\frac{\frac{6x+7}{x+1}}{5-\frac{3}{x-3}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{x-3}{x-3}.

$$\frac{\frac{6x+7}{x+1}}{\frac{5\left(x-3\right)}{x-3}-\frac{3}{x-3}}$$

Since \frac{5\left(x-3\right)}{x-3} and \frac{3}{x-3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{6x+7}{x+1}}{\frac{5\left(x-3\right)-3}{x-3}}$$

Do the multiplications in 5\left(x-3\right)-3.

$$\frac{\frac{6x+7}{x+1}}{\frac{5x-15-3}{x-3}}$$

Combine like terms in 5x-15-3.

$$\frac{\frac{6x+7}{x+1}}{\frac{5x-18}{x-3}}$$

Divide \frac{6x+7}{x+1} by \frac{5x-18}{x-3} by multiplying \frac{6x+7}{x+1} by the reciprocal of \frac{5x-18}{x-3}.

$$\frac{\left(6x+7\right)\left(x-3\right)}{\left(x+1\right)\left(5x-18\right)}$$

Apply the distributive property by multiplying each term of 6x+7 by each term of x-3.

$$\frac{6x^{2}-18x+7x-21}{\left(x+1\right)\left(5x-18\right)}$$

Combine -18x and 7x to get -11x.

$$\frac{6x^{2}-11x-21}{\left(x+1\right)\left(5x-18\right)}$$

Apply the distributive property by multiplying each term of x+1 by each term of 5x-18.

$$\frac{6x^{2}-11x-21}{5x^{2}-18x+5x-18}$$

Combine -18x and 5x to get -13x.

$$\frac{6x^{2}-11x-21}{5x^{2}-13x-18}$$