Solve n1/t+1/t+40=1/48

$$n \frac { 1 } { t } + \frac { 1 } { t + 40 } = \frac { 1 } { 48 }$$

Solve for n

$$n=-\frac{t\left(8-t\right)}{48\left(t+40\right)}$$

$$t\neq 0\text{ and }t\neq -40$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 48t\left(t+40\right), the least common multiple of t,t+40,48.

$$n\left(48t+1920\right)\times 1+48t=t\left(t+40\right)$$

Use the distributive property to multiply n by 48t+1920.

$$\left(48nt+1920n\right)\times 1+48t=t\left(t+40\right)$$

Use the distributive property to multiply 48nt+1920n by 1.

$$48nt+1920n+48t=t\left(t+40\right)$$

Use the distributive property to multiply t by t+40.

$$48nt+1920n+48t=t^{2}+40t$$

Subtract 48t from both sides.

$$48nt+1920n=t^{2}+40t-48t$$

Combine 40t and -48t to get -8t.

$$48nt+1920n=t^{2}-8t$$

Combine all terms containing n.

$$\left(48t+1920\right)n=t^{2}-8t$$

Divide both sides by 48t+1920.

$$\frac{\left(48t+1920\right)n}{48t+1920}=\frac{t\left(t-8\right)}{48t+1920}$$

Dividing by 48t+1920 undoes the multiplication by 48t+1920.

$$n=\frac{t\left(t-8\right)}{48t+1920}$$

Divide t\left(-8+t\right) by 48t+1920.

$$n=\frac{t\left(t-8\right)}{48\left(t+40\right)}$$

Solve for t

$$\left\{\begin{matrix}t=4\sqrt{36n^{2}+132n+1}+24n+4\text{, }&n\geq \frac{\sqrt{30}}{3}-\frac{11}{6}\text{ or }n\leq -\frac{\sqrt{30}}{3}-\frac{11}{6}\\t=-4\sqrt{36n^{2}+132n+1}+24n+4\text{, }&\left(n\neq 0\text{ and }n\geq \frac{\sqrt{30}}{3}-\frac{11}{6}\right)\text{ or }n\leq -\frac{\sqrt{30}}{3}-\frac{11}{6}\end{matrix}\right.$$