Solve 4x-3/2x+1-10(2x-1/4x-3)

$$\frac { 4 x - 3 } { 2 x + 1 } - 10 ( \frac { 2 x - 1 } { 4 x - 3 } )$$

Evaluate

$$-\frac{24x^{2}+24x-19}{\left(4x-3\right)\left(2x+1\right)}$$

Short Solution Steps

Express 10\times \frac{2x-1}{4x-3} as a single fraction.

$$\frac{4x-3}{2x+1}-\frac{10\left(2x-1\right)}{4x-3}$$

Use the distributive property to multiply 10 by 2x-1.

$$\frac{4x-3}{2x+1}-\frac{20x-10}{4x-3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x+1 and 4x-3 is \left(4x-3\right)\left(2x+1\right). Multiply \frac{4x-3}{2x+1} times \frac{4x-3}{4x-3}. Multiply \frac{20x-10}{4x-3} times \frac{2x+1}{2x+1}.

$$\frac{\left(4x-3\right)\left(4x-3\right)}{\left(4x-3\right)\left(2x+1\right)}-\frac{\left(20x-10\right)\left(2x+1\right)}{\left(4x-3\right)\left(2x+1\right)}$$

Since \frac{\left(4x-3\right)\left(4x-3\right)}{\left(4x-3\right)\left(2x+1\right)} and \frac{\left(20x-10\right)\left(2x+1\right)}{\left(4x-3\right)\left(2x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(4x-3\right)\left(4x-3\right)-\left(20x-10\right)\left(2x+1\right)}{\left(4x-3\right)\left(2x+1\right)}$$

Do the multiplications in \left(4x-3\right)\left(4x-3\right)-\left(20x-10\right)\left(2x+1\right).

$$\frac{16x^{2}-12x-12x+9-40x^{2}-20x+20x+10}{\left(4x-3\right)\left(2x+1\right)}$$

Combine like terms in 16x^{2}-12x-12x+9-40x^{2}-20x+20x+10.

$$\frac{-24x^{2}-24x+19}{\left(4x-3\right)\left(2x+1\right)}$$

Expand \left(4x-3\right)\left(2x+1\right).

$$\frac{-24x^{2}-24x+19}{8x^{2}-2x-3}$$

Expand

$$\frac{19-24x-24x^{2}}{\left(4x-3\right)\left(2x+1\right)}$$

Short Solution Steps

Express 10\times \frac{2x-1}{4x-3} as a single fraction.

$$\frac{4x-3}{2x+1}-\frac{10\left(2x-1\right)}{4x-3}$$

Use the distributive property to multiply 10 by 2x-1.

$$\frac{4x-3}{2x+1}-\frac{20x-10}{4x-3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x+1 and 4x-3 is \left(4x-3\right)\left(2x+1\right). Multiply \frac{4x-3}{2x+1} times \frac{4x-3}{4x-3}. Multiply \frac{20x-10}{4x-3} times \frac{2x+1}{2x+1}.

$$\frac{\left(4x-3\right)\left(4x-3\right)}{\left(4x-3\right)\left(2x+1\right)}-\frac{\left(20x-10\right)\left(2x+1\right)}{\left(4x-3\right)\left(2x+1\right)}$$

Since \frac{\left(4x-3\right)\left(4x-3\right)}{\left(4x-3\right)\left(2x+1\right)} and \frac{\left(20x-10\right)\left(2x+1\right)}{\left(4x-3\right)\left(2x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(4x-3\right)\left(4x-3\right)-\left(20x-10\right)\left(2x+1\right)}{\left(4x-3\right)\left(2x+1\right)}$$

Do the multiplications in \left(4x-3\right)\left(4x-3\right)-\left(20x-10\right)\left(2x+1\right).

$$\frac{16x^{2}-12x-12x+9-40x^{2}-20x+20x+10}{\left(4x-3\right)\left(2x+1\right)}$$

Combine like terms in 16x^{2}-12x-12x+9-40x^{2}-20x+20x+10.

$$\frac{-24x^{2}-24x+19}{\left(4x-3\right)\left(2x+1\right)}$$

Expand \left(4x-3\right)\left(2x+1\right).

$$\frac{-24x^{2}-24x+19}{8x^{2}-2x-3}$$