Solve 6x-1/2x-6-1-2x/6x+1-28x^2+20x+11/12x^2-34x-6

$$\frac { 6 x - 1 } { 2 x - 6 } - \frac { 1 - 2 x } { 6 x + 1 } - \frac { 28 x ^ { 2 } + 20 x + 11 } { 12 x ^ { 2 } - 34 x - 6 }$$

Evaluate

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Short Solution Steps

Factor 2x-6.

$$\frac{6x-1}{2\left(x-3\right)}-\frac{1-2x}{6x+1}-\frac{28x^{2}+20x+11}{12x^{2}-34x-6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x-3\right) and 6x+1 is 2\left(x-3\right)\left(6x+1\right). Multiply \frac{6x-1}{2\left(x-3\right)} times \frac{6x+1}{6x+1}. Multiply \frac{1-2x}{6x+1} times \frac{2\left(x-3\right)}{2\left(x-3\right)}.

$$\frac{\left(6x-1\right)\left(6x+1\right)}{2\left(x-3\right)\left(6x+1\right)}-\frac{\left(1-2x\right)\times 2\left(x-3\right)}{2\left(x-3\right)\left(6x+1\right)}-\frac{28x^{2}+20x+11}{12x^{2}-34x-6}$$

Since \frac{\left(6x-1\right)\left(6x+1\right)}{2\left(x-3\right)\left(6x+1\right)} and \frac{\left(1-2x\right)\times 2\left(x-3\right)}{2\left(x-3\right)\left(6x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(6x-1\right)\left(6x+1\right)-\left(1-2x\right)\times 2\left(x-3\right)}{2\left(x-3\right)\left(6x+1\right)}-\frac{28x^{2}+20x+11}{12x^{2}-34x-6}$$

Do the multiplications in \left(6x-1\right)\left(6x+1\right)-\left(1-2x\right)\times 2\left(x-3\right).

$$\frac{36x^{2}+6x-6x-1-2x+6+4x^{2}-12x}{2\left(x-3\right)\left(6x+1\right)}-\frac{28x^{2}+20x+11}{12x^{2}-34x-6}$$

Combine like terms in 36x^{2}+6x-6x-1-2x+6+4x^{2}-12x.

$$\frac{40x^{2}-14x+5}{2\left(x-3\right)\left(6x+1\right)}-\frac{28x^{2}+20x+11}{12x^{2}-34x-6}$$

Factor 12x^{2}-34x-6.

$$\frac{40x^{2}-14x+5}{2\left(x-3\right)\left(6x+1\right)}-\frac{28x^{2}+20x+11}{2\left(x-3\right)\left(6x+1\right)}$$

Since \frac{40x^{2}-14x+5}{2\left(x-3\right)\left(6x+1\right)} and \frac{28x^{2}+20x+11}{2\left(x-3\right)\left(6x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{40x^{2}-14x+5-\left(28x^{2}+20x+11\right)}{2\left(x-3\right)\left(6x+1\right)}$$

Do the multiplications in 40x^{2}-14x+5-\left(28x^{2}+20x+11\right).

$$\frac{40x^{2}-14x+5-28x^{2}-20x-11}{2\left(x-3\right)\left(6x+1\right)}$$

Combine like terms in 40x^{2}-14x+5-28x^{2}-20x-11.

$$\frac{12x^{2}-34x-6}{2\left(x-3\right)\left(6x+1\right)}$$

Factor the expressions that are not already factored in \frac{12x^{2}-34x-6}{2\left(x-3\right)\left(6x+1\right)}.

$$\frac{2\left(x-3\right)\left(6x+1\right)}{2\left(x-3\right)\left(6x+1\right)}$$

Cancel out 2\left(x-3\right)\left(6x+1\right) in both numerator and denominator.

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Factor

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