Solve 1/(n + 80) + 1/(n + 20) = 1/n | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{1}{n+80}+\frac{1}{n+20}=\frac{1}{n}$$

Solve for n

$n=-40$
$n=40$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Variable $n$ cannot be equal to any of the values $-80,-20,0$ since division by zero is not defined. Multiply both sides of the equation by $n\left(n+20\right)\left(n+80\right)$, the least common multiple of $n+80,n+20,n$.

$$n\left(n+20\right)+n\left(n+80\right)=\left(n+20\right)\left(n+80\right)$$

Use the distributive property to multiply $n$ by $n+20$.

$$n^{2}+20n+n\left(n+80\right)=\left(n+20\right)\left(n+80\right)$$

Use the distributive property to multiply $n$ by $n+80$.

$$n^{2}+20n+n^{2}+80n=\left(n+20\right)\left(n+80\right)$$

Combine $n^{2}$ and $n^{2}$ to get $2n^{2}$.

$$2n^{2}+20n+80n=\left(n+20\right)\left(n+80\right)$$

Combine $20n$ and $80n$ to get $100n$.

$$2n^{2}+100n=\left(n+20\right)\left(n+80\right)$$

Use the distributive property to multiply $n+20$ by $n+80$ and combine like terms.

$$2n^{2}+100n=n^{2}+100n+1600$$

Subtract $n^{2}$ from both sides.

$$2n^{2}+100n-n^{2}=100n+1600$$

Combine $2n^{2}$ and $-n^{2}$ to get $n^{2}$.

$$n^{2}+100n=100n+1600$$

Subtract $100n$ from both sides.

$$n^{2}+100n-100n=1600$$

Combine $100n$ and $-100n$ to get $0$.

$$n^{2}=1600$$

Take the square root of both sides of the equation.

$$n=40$$ $$n=-40$$

Steps Using the Quadratic Formula

Variable $n$ cannot be equal to any of the values $-80,-20,0$ since division by zero is not defined. Multiply both sides of the equation by $n\left(n+20\right)\left(n+80\right)$, the least common multiple of $n+80,n+20,n$.

$$n\left(n+20\right)+n\left(n+80\right)=\left(n+20\right)\left(n+80\right)$$

Use the distributive property to multiply $n$ by $n+20$.

$$n^{2}+20n+n\left(n+80\right)=\left(n+20\right)\left(n+80\right)$$

Use the distributive property to multiply $n$ by $n+80$.

$$n^{2}+20n+n^{2}+80n=\left(n+20\right)\left(n+80\right)$$

Combine $n^{2}$ and $n^{2}$ to get $2n^{2}$.

$$2n^{2}+20n+80n=\left(n+20\right)\left(n+80\right)$$

Combine $20n$ and $80n$ to get $100n$.

$$2n^{2}+100n=\left(n+20\right)\left(n+80\right)$$

Use the distributive property to multiply $n+20$ by $n+80$ and combine like terms.

$$2n^{2}+100n=n^{2}+100n+1600$$

Subtract $n^{2}$ from both sides.

$$2n^{2}+100n-n^{2}=100n+1600$$

Combine $2n^{2}$ and $-n^{2}$ to get $n^{2}$.

$$n^{2}+100n=100n+1600$$

Subtract $100n$ from both sides.

$$n^{2}+100n-100n=1600$$

Combine $100n$ and $-100n$ to get $0$.

$$n^{2}=1600$$

Subtract $1600$ from both sides.

$$n^{2}-1600=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-1600$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$n=\frac{0±\sqrt{0^{2}-4\left(-1600\right)}}{2}$$

Square $0$.

$$n=\frac{0±\sqrt{-4\left(-1600\right)}}{2}$$

Multiply $-4$ times $-1600$.

$$n=\frac{0±\sqrt{6400}}{2}$$

Take the square root of $6400$.

$$n=\frac{0±80}{2}$$

Now solve the equation $n=\frac{0±80}{2}$ when $±$ is plus. Divide $80$ by $2$.

$$n=40$$

Now solve the equation $n=\frac{0±80}{2}$ when $±$ is minus. Divide $-80$ by $2$.

$$n=-40$$

The equation is now solved.

$$n=40$$ $$n=-40$$