Solve f(x)=1/frac{4{x+3}-2}

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x+3}{x+3}.

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

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

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

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

$$\frac{1}{\frac{4-2x-6}{x+3}}$$

Combine like terms in 4-2x-6.

$$\frac{1}{\frac{-2-2x}{x+3}}$$

Divide 1 by \frac{-2-2x}{x+3} by multiplying 1 by the reciprocal of \frac{-2-2x}{x+3}.

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

Factor

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