Solve 4x+5/36x^2+24x-12-40x-7/36x^2+24x-12

$$\frac { 4 x + 5 } { 36 x ^ { 2 } + 24 x - 12 } - \frac { 40 x - 7 } { 36 x ^ { 2 } + 24 x - 12 }$$

Evaluate

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

Short Solution Steps

Since \frac{4x+5}{36x^{2}+24x-12} and \frac{40x-7}{36x^{2}+24x-12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4x+5-\left(40x-7\right)}{36x^{2}+24x-12}$$

Do the multiplications in 4x+5-\left(40x-7\right).

$$\frac{4x+5-40x+7}{36x^{2}+24x-12}$$

Combine like terms in 4x+5-40x+7.

$$\frac{-36x+12}{36x^{2}+24x-12}$$

Factor the expressions that are not already factored in \frac{-36x+12}{36x^{2}+24x-12}.

$$\frac{12\left(-3x+1\right)}{12\left(3x-1\right)\left(x+1\right)}$$

Extract the negative sign in 1-3x.

$$\frac{-12\left(3x-1\right)}{12\left(3x-1\right)\left(x+1\right)}$$

Cancel out 12\left(3x-1\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

Since \frac{4x+5}{36x^{2}+24x-12} and \frac{40x-7}{36x^{2}+24x-12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4x+5-\left(40x-7\right)}{36x^{2}+24x-12}$$

Do the multiplications in 4x+5-\left(40x-7\right).

$$\frac{4x+5-40x+7}{36x^{2}+24x-12}$$

Combine like terms in 4x+5-40x+7.

$$\frac{-36x+12}{36x^{2}+24x-12}$$

Factor the expressions that are not already factored in \frac{-36x+12}{36x^{2}+24x-12}.

$$\frac{12\left(-3x+1\right)}{12\left(3x-1\right)\left(x+1\right)}$$

Extract the negative sign in 1-3x.

$$\frac{-12\left(3x-1\right)}{12\left(3x-1\right)\left(x+1\right)}$$

Cancel out 12\left(3x-1\right) in both numerator and denominator.

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