Solve {l}{1/f=1/3+1/4}{g=f}{text{Solvefor}htext{where}}{h=g}

$$\left. \begin{array} { l } { \frac{1}{f} = \frac{1}{3} + \frac{1}{4} }\\ { g = f }\\ { \text{Solve for } h \text{ where} } \\ { h = g } \end{array} \right.$$

Solve for f, g, h

$$h = \frac{12}{7} = 1\frac{5}{7} \approx 1.714285714$$

Solution Steps

Consider the first equation. Variable f cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12f, the least common multiple of f,3,4.

$$12=12f\times \frac{1}{3}+12f\times \frac{1}{4}$$

Multiply 12 and \frac{1}{3} to get 4.

$$12=4f+12f\times \frac{1}{4}$$

Multiply 12 and \frac{1}{4} to get 3.

$$12=4f+3f$$

Combine 4f and 3f to get 7f.

$$12=7f$$

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

$$7f=12$$

Divide both sides by 7.

$$f=\frac{12}{7}$$

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

$$g=\frac{12}{7}$$

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

$$h=\frac{12}{7}$$

The system is now solved.

$$f=\frac{12}{7} g=\frac{12}{7} h=\frac{12}{7}$$