Solve {l}{1/x+1=4/3}{text{Solvefor}ytext{where}}{y=1/x+1/x+2}

$$\left. \begin{array} { l } { \frac{1}{x + 1} = \frac{4}{3} }\\ { \text{Solve for } y \text{ where} } \\ { y = \frac{1}{x} + \frac{1}{x + 2} } \end{array} \right.$$

Solve for x, y

$$y = -\frac{24}{7} = -3\frac{3}{7} \approx -3.428571429$$

Solution Steps

Consider the first equation. Variable x cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by 3\left(x+1\right), the least common multiple of x+1,3.

$$3=4\left(x+1\right)$$

Use the distributive property to multiply 4 by x+1.

$$3=4x+4$$

Swap sides so that all variable terms are on the left hand side.

$$4x+4=3$$

Subtract 4 from both sides.

$$4x=3-4$$

Subtract 4 from 3 to get -1.

$$4x=-1$$

Divide both sides by 4.

$$x=-\frac{1}{4}$$

Consider the second equation. Insert the known values of variables into the equation.

$$y=\frac{1}{-\frac{1}{4}}+\frac{1}{-\frac{1}{4}+2}$$

Divide 1 by -\frac{1}{4} by multiplying 1 by the reciprocal of -\frac{1}{4}.

$$y=1\left(-4\right)+\frac{1}{-\frac{1}{4}+2}$$

Multiply 1 and -4 to get -4.

$$y=-4+\frac{1}{-\frac{1}{4}+2}$$

Add -\frac{1}{4} and 2 to get \frac{7}{4}.

$$y=-4+\frac{1}{\frac{7}{4}}$$

Divide 1 by \frac{7}{4} by multiplying 1 by the reciprocal of \frac{7}{4}.

$$y=-4+1\times \frac{4}{7}$$

Multiply 1 and \frac{4}{7} to get \frac{4}{7}.

$$y=-4+\frac{4}{7}$$

Add -4 and \frac{4}{7} to get -\frac{24}{7}.

$$y=-\frac{24}{7}$$

The system is now solved.

$$x=-\frac{1}{4} y=-\frac{24}{7}$$