Solve 5/m-x/m+1=3

$$\frac { 5 } { m } - \frac { x } { m + 1 } = 3$$

Solve for x

$$x=-3m+2+\frac{5}{m}$$

$$m\neq 0\text{ and }m\neq -1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by m\left(m+1\right), the least common multiple of m,m+1.

$$\left(m+1\right)\times 5-mx=3m\left(m+1\right)$$

Use the distributive property to multiply m+1 by 5.

$$5m+5-mx=3m\left(m+1\right)$$

Use the distributive property to multiply 3m by m+1.

$$5m+5-mx=3m^{2}+3m$$

Subtract 5m from both sides.

$$5-mx=3m^{2}+3m-5m$$

Combine 3m and -5m to get -2m.

$$5-mx=3m^{2}-2m$$

Subtract 5 from both sides.

$$-mx=3m^{2}-2m-5$$

The equation is in standard form.

$$\left(-m\right)x=3m^{2}-2m-5$$

Divide both sides by -m.

$$\frac{\left(-m\right)x}{-m}=\frac{\left(3m-5\right)\left(m+1\right)}{-m}$$

Dividing by -m undoes the multiplication by -m.

$$x=\frac{\left(3m-5\right)\left(m+1\right)}{-m}$$

Divide \left(-5+3m\right)\left(1+m\right) by -m.

$$x=-3m+2+\frac{5}{m}$$

Solve for m

$$\left\{\begin{matrix}\\m=\frac{\sqrt{x^{2}-4x+64}}{6}-\frac{x}{6}+\frac{1}{3}\text{, }&\text{unconditionally}\\m=-\frac{\sqrt{x^{2}-4x+64}}{6}-\frac{x}{6}+\frac{1}{3}\text{, }&x\neq 0\end{matrix}\right.$$