Solve 6x-11/1-frac{3x+7{4x+1}}

$$\frac { 6 x - 11 } { 1 - \frac { 3 x + 7 } { 4 x + 1 } }$$

Evaluate

$$\frac{\left(6x-11\right)\left(4x+1\right)}{x-6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{4x+1}{4x+1}.

$$\frac{6x-11}{\frac{4x+1}{4x+1}-\frac{3x+7}{4x+1}}$$

Since \frac{4x+1}{4x+1} and \frac{3x+7}{4x+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6x-11}{\frac{4x+1-\left(3x+7\right)}{4x+1}}$$

Do the multiplications in 4x+1-\left(3x+7\right).

$$\frac{6x-11}{\frac{4x+1-3x-7}{4x+1}}$$

Combine like terms in 4x+1-3x-7.

$$\frac{6x-11}{\frac{x-6}{4x+1}}$$

Divide 6x-11 by \frac{x-6}{4x+1} by multiplying 6x-11 by the reciprocal of \frac{x-6}{4x+1}.

$$\frac{\left(6x-11\right)\left(4x+1\right)}{x-6}$$

Apply the distributive property by multiplying each term of 6x-11 by each term of 4x+1.

$$\frac{24x^{2}+6x-44x-11}{x-6}$$

Combine 6x and -44x to get -38x.

$$\frac{24x^{2}-38x-11}{x-6}$$

Expand

$$\frac{24x^{2}-38x-11}{x-6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{4x+1}{4x+1}.

$$\frac{6x-11}{\frac{4x+1}{4x+1}-\frac{3x+7}{4x+1}}$$

Since \frac{4x+1}{4x+1} and \frac{3x+7}{4x+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6x-11}{\frac{4x+1-\left(3x+7\right)}{4x+1}}$$

Do the multiplications in 4x+1-\left(3x+7\right).

$$\frac{6x-11}{\frac{4x+1-3x-7}{4x+1}}$$

Combine like terms in 4x+1-3x-7.

$$\frac{6x-11}{\frac{x-6}{4x+1}}$$

Divide 6x-11 by \frac{x-6}{4x+1} by multiplying 6x-11 by the reciprocal of \frac{x-6}{4x+1}.

$$\frac{\left(6x-11\right)\left(4x+1\right)}{x-6}$$

Apply the distributive property by multiplying each term of 6x-11 by each term of 4x+1.

$$\frac{24x^{2}+6x-44x-11}{x-6}$$

Combine 6x and -44x to get -38x.

$$\frac{24x^{2}-38x-11}{x-6}$$