Solve x^2-9x=4x^2-11mx+3m/m+1

$$x ^ { 2 } - 9 x = \frac { 4 x ^ { 2 } - 11 m x + 3 m } { m + 1 }$$

Solve for m

$$\left\{\begin{matrix}m=\frac{3x}{x-1}\text{, }&x\neq \frac{1}{4}\text{ and }x\neq 1\\m\neq -1\text{, }&x=-3\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable m cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by m+1.

$$\left(m+1\right)x^{2}-9x\left(m+1\right)=4x^{2}-11mx+3m$$

Use the distributive property to multiply m+1 by x^{2}.

$$mx^{2}+x^{2}-9x\left(m+1\right)=4x^{2}-11mx+3m$$

Use the distributive property to multiply -9x by m+1.

$$mx^{2}+x^{2}-9xm-9x=4x^{2}-11mx+3m$$

Add 11mx to both sides.

$$mx^{2}+x^{2}-9xm-9x+11mx=4x^{2}+3m$$

Combine -9xm and 11mx to get 2xm.

$$mx^{2}+x^{2}+2xm-9x=4x^{2}+3m$$

Subtract 3m from both sides.

$$mx^{2}+x^{2}+2xm-9x-3m=4x^{2}$$

Subtract x^{2} from both sides.

$$mx^{2}+2xm-9x-3m=4x^{2}-x^{2}$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$mx^{2}+2xm-9x-3m=3x^{2}$$

Add 9x to both sides.

$$mx^{2}+2xm-3m=3x^{2}+9x$$

Combine all terms containing m.

$$\left(x^{2}+2x-3\right)m=3x^{2}+9x$$

Divide both sides by x^{2}+2x-3.

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

Dividing by x^{2}+2x-3 undoes the multiplication by x^{2}+2x-3.

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

Divide 3x\left(3+x\right) by x^{2}+2x-3.

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

Variable m cannot be equal to -1.

$$m=\frac{3x}{x-1}\text{, }m\neq -1$$

Solve for x

$$\left\{\begin{matrix}x=-3\text{, }&m\neq -1\\x=\frac{m}{m-3}\text{, }&m\neq 3\text{ and }m\neq -1\end{matrix}\right.$$