Solve 4x/4x^2-7x-2-1/x-2=

$$\frac { 4 x } { 4 x ^ { 2 } - 7 x - 2 } - \frac { 1 } { x - 2 } =$$

Evaluate

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

Short Solution Steps

Factor 4x^{2}-7x-2.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-2\right)\left(4x+1\right) and x-2 is \left(x-2\right)\left(4x+1\right). Multiply \frac{1}{x-2} times \frac{4x+1}{4x+1}.

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

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

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

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

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

Combine like terms in 4x-4x-1.

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

Expand \left(x-2\right)\left(4x+1\right).

$$\frac{-1}{4x^{2}-7x-2}$$

Differentiate w.r.t. x

$$\frac{8x-7}{\left(\left(x-2\right)\left(4x+1\right)\right)^{2}}$$