Solve n/5-n+2n-5/n=1

$$\frac { n } { 5 - n } + \frac { 2 n - 5 } { n } = 1$$

Solve for n

$$n = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

Variable n cannot be equal to any of the values 0,5 since division by zero is not defined. Multiply both sides of the equation by n\left(n-5\right), the least common multiple of 5-n,n.

$$-nn+\left(n-5\right)\left(2n-5\right)=n\left(n-5\right)$$

Multiply n and n to get n^{2}.

$$-n^{2}+\left(n-5\right)\left(2n-5\right)=n\left(n-5\right)$$

Use the distributive property to multiply n-5 by 2n-5 and combine like terms.

$$-n^{2}+2n^{2}-15n+25=n\left(n-5\right)$$

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

$$n^{2}-15n+25=n\left(n-5\right)$$

Use the distributive property to multiply n by n-5.

$$n^{2}-15n+25=n^{2}-5n$$

Subtract n^{2} from both sides.

$$n^{2}-15n+25-n^{2}=-5n$$

Combine n^{2} and -n^{2} to get 0.

$$-15n+25=-5n$$

Add 5n to both sides.

$$-15n+25+5n=0$$

Combine -15n and 5n to get -10n.

$$-10n+25=0$$

Subtract 25 from both sides. Anything subtracted from zero gives its negation.

$$-10n=-25$$

Divide both sides by -10.

$$n=\frac{-25}{-10}$$

Reduce the fraction \frac{-25}{-10} to lowest terms by extracting and canceling out -5.

$$n=\frac{5}{2}$$