Solve 4/x-3+3/frac{4x-1{x-3}+4}

$$\frac { \frac { 4 } { x - 3 } + 3 } { \frac { 4 x - 1 } { x - 3 } + 4 }$$

Evaluate

$$\frac{3x-5}{8x-13}$$

Short Solution Steps

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

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

Since \frac{4}{x-3} and \frac{3\left(x-3\right)}{x-3} have the same denominator, add them by adding their numerators.

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

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

$$\frac{\frac{4+3x-9}{x-3}}{\frac{4x-1}{x-3}+4}$$

Combine like terms in 4+3x-9.

$$\frac{\frac{-5+3x}{x-3}}{\frac{4x-1}{x-3}+4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x-3}{x-3}.

$$\frac{\frac{-5+3x}{x-3}}{\frac{4x-1}{x-3}+\frac{4\left(x-3\right)}{x-3}}$$

Since \frac{4x-1}{x-3} and \frac{4\left(x-3\right)}{x-3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-5+3x}{x-3}}{\frac{4x-1+4\left(x-3\right)}{x-3}}$$

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

$$\frac{\frac{-5+3x}{x-3}}{\frac{4x-1+4x-12}{x-3}}$$

Combine like terms in 4x-1+4x-12.

$$\frac{\frac{-5+3x}{x-3}}{\frac{8x-13}{x-3}}$$

Divide \frac{-5+3x}{x-3} by \frac{8x-13}{x-3} by multiplying \frac{-5+3x}{x-3} by the reciprocal of \frac{8x-13}{x-3}.

$$\frac{\left(-5+3x\right)\left(x-3\right)}{\left(x-3\right)\left(8x-13\right)}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{3x-5}{8x-13}$$

Expand

$$\frac{3x-5}{8x-13}$$

Short Solution Steps

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

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

Since \frac{4}{x-3} and \frac{3\left(x-3\right)}{x-3} have the same denominator, add them by adding their numerators.

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

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

$$\frac{\frac{4+3x-9}{x-3}}{\frac{4x-1}{x-3}+4}$$

Combine like terms in 4+3x-9.

$$\frac{\frac{-5+3x}{x-3}}{\frac{4x-1}{x-3}+4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x-3}{x-3}.

$$\frac{\frac{-5+3x}{x-3}}{\frac{4x-1}{x-3}+\frac{4\left(x-3\right)}{x-3}}$$

Since \frac{4x-1}{x-3} and \frac{4\left(x-3\right)}{x-3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-5+3x}{x-3}}{\frac{4x-1+4\left(x-3\right)}{x-3}}$$

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

$$\frac{\frac{-5+3x}{x-3}}{\frac{4x-1+4x-12}{x-3}}$$

Combine like terms in 4x-1+4x-12.

$$\frac{\frac{-5+3x}{x-3}}{\frac{8x-13}{x-3}}$$

Divide \frac{-5+3x}{x-3} by \frac{8x-13}{x-3} by multiplying \frac{-5+3x}{x-3} by the reciprocal of \frac{8x-13}{x-3}.

$$\frac{\left(-5+3x\right)\left(x-3\right)}{\left(x-3\right)\left(8x-13\right)}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{3x-5}{8x-13}$$