Solve [(x+4)divx^2+5x+4/x-1]+3

$$[ ( x + 4 ) \div \frac { x ^ { 2 } + 5 x + 4 } { x - 1 } ] + 3$$

Evaluate

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

Short Solution Steps

Divide x+4 by \frac{x^{2}+5x+4}{x-1} by multiplying x+4 by the reciprocal of \frac{x^{2}+5x+4}{x-1}.

$$\frac{\left(x+4\right)\left(x-1\right)}{x^{2}+5x+4}+3$$

Factor the expressions that are not already factored in \frac{\left(x+4\right)\left(x-1\right)}{x^{2}+5x+4}.

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

Cancel out x+4 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x+1}{x+1}.

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

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

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

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

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

Combine like terms in x-1+3x+3.

$$\frac{4x+2}{x+1}$$

Expand

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

Short Solution Steps

Divide x+4 by \frac{x^{2}+5x+4}{x-1} by multiplying x+4 by the reciprocal of \frac{x^{2}+5x+4}{x-1}.

$$\frac{\left(x+4\right)\left(x-1\right)}{x^{2}+5x+4}+3$$

Factor the expressions that are not already factored in \frac{\left(x+4\right)\left(x-1\right)}{x^{2}+5x+4}.

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

Cancel out x+4 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x+1}{x+1}.

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

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

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

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

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

Combine like terms in x-1+3x+3.

$$\frac{4x+2}{x+1}$$