Solve -2x-5/5x-3+6x-16/6-10x

$$\frac{ -2x-5 }{ 5x-3 } + \frac{ 6x-16 }{ 6-10x }$$

Evaluate

$$-1$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{6x-16}{6-10x}.

$$\frac{-2x-5}{5x-3}+\frac{2\left(3x-8\right)}{2\left(-5x+3\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-2x-5}{5x-3}+\frac{3x-8}{-5x+3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5x-3 and -5x+3 is 5x-3. Multiply \frac{3x-8}{-5x+3} times \frac{-1}{-1}.

$$\frac{-2x-5}{5x-3}+\frac{-\left(3x-8\right)}{5x-3}$$

Since \frac{-2x-5}{5x-3} and \frac{-\left(3x-8\right)}{5x-3} have the same denominator, add them by adding their numerators.

$$\frac{-2x-5-\left(3x-8\right)}{5x-3}$$

Do the multiplications in -2x-5-\left(3x-8\right).

$$\frac{-2x-5-3x+8}{5x-3}$$

Combine like terms in -2x-5-3x+8.

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

Extract the negative sign in -5x+3.

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

Cancel out 5x-3 in both numerator and denominator.

$$-1$$

Factor

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