Solve yc/x+90/x+9=11/2

$$\frac { y c } { x } + \frac { 90 } { x + 9 } = \frac { 11 } { 2 }$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=-\frac{x\left(81-11x\right)}{2y\left(x+9\right)}\text{, }&x\neq -9\text{ and }y\neq 0\text{ and }x\neq 0\\c\in \mathrm{C}\text{, }&x=\frac{81}{11}\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x\left(x+9\right), the least common multiple of x,x+9,2.

$$\left(2x+18\right)yc+2x\times 90=11x\left(x+9\right)$$

Use the distributive property to multiply 2x+18 by y.

$$\left(2xy+18y\right)c+2x\times 90=11x\left(x+9\right)$$

Use the distributive property to multiply 2xy+18y by c.

$$2xyc+18yc+2x\times 90=11x\left(x+9\right)$$

Multiply 2 and 90 to get 180.

$$2xyc+18yc+180x=11x\left(x+9\right)$$

Use the distributive property to multiply 11x by x+9.

$$2xyc+18yc+180x=11x^{2}+99x$$

Subtract 180x from both sides.

$$2xyc+18yc=11x^{2}+99x-180x$$

Combine 99x and -180x to get -81x.

$$2xyc+18yc=11x^{2}-81x$$

Combine all terms containing c.

$$\left(2xy+18y\right)c=11x^{2}-81x$$

Divide both sides by 18y+2yx.

$$\frac{\left(2xy+18y\right)c}{2xy+18y}=\frac{x\left(11x-81\right)}{2xy+18y}$$

Dividing by 18y+2yx undoes the multiplication by 18y+2yx.

$$c=\frac{x\left(11x-81\right)}{2xy+18y}$$

Divide x\left(-81+11x\right) by 18y+2yx.

$$c=\frac{x\left(11x-81\right)}{2y\left(x+9\right)}$$

Solve for c

$$\left\{\begin{matrix}c=-\frac{x\left(81-11x\right)}{2y\left(x+9\right)}\text{, }&x\neq -9\text{ and }y\neq 0\text{ and }x\neq 0\\c\in \mathrm{R}\text{, }&x=\frac{81}{11}\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x\left(x+9\right), the least common multiple of x,x+9,2.

$$\left(2x+18\right)yc+2x\times 90=11x\left(x+9\right)$$

Use the distributive property to multiply 2x+18 by y.

$$\left(2xy+18y\right)c+2x\times 90=11x\left(x+9\right)$$

Use the distributive property to multiply 2xy+18y by c.

$$2xyc+18yc+2x\times 90=11x\left(x+9\right)$$

Multiply 2 and 90 to get 180.

$$2xyc+18yc+180x=11x\left(x+9\right)$$

Use the distributive property to multiply 11x by x+9.

$$2xyc+18yc+180x=11x^{2}+99x$$

Subtract 180x from both sides.

$$2xyc+18yc=11x^{2}+99x-180x$$

Combine 99x and -180x to get -81x.

$$2xyc+18yc=11x^{2}-81x$$

Combine all terms containing c.

$$\left(2xy+18y\right)c=11x^{2}-81x$$

Divide both sides by 18y+2yx.

$$\frac{\left(2xy+18y\right)c}{2xy+18y}=\frac{x\left(11x-81\right)}{2xy+18y}$$

Dividing by 18y+2yx undoes the multiplication by 18y+2yx.

$$c=\frac{x\left(11x-81\right)}{2xy+18y}$$

Divide x\left(-81+11x\right) by 18y+2yx.

$$c=\frac{x\left(11x-81\right)}{2y\left(x+9\right)}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=\frac{\sqrt{1116cy+4\left(cy\right)^{2}+6561}}{22}+\frac{cy}{11}+\frac{81}{22}\text{, }&\text{unconditionally}\\x=-\frac{\sqrt{1116cy+4\left(cy\right)^{2}+6561}}{22}+\frac{cy}{11}+\frac{81}{22}\text{, }&y\neq 0\text{ and }c\neq 0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{1116cy+4\left(cy\right)^{2}+6561}+2cy+81}{22}\text{, }&y\leq -\frac{18\sqrt{55}|c|+\frac{279c}{2}}{c^{2}}\text{ or }y\geq \frac{18\sqrt{55}|c|-\frac{279c}{2}}{c^{2}}\text{ or }c=0\\x=\frac{-\sqrt{1116cy+4\left(cy\right)^{2}+6561}+2cy+81}{22}\text{, }&\left(y\geq \frac{18\sqrt{55}|c|-\frac{279c}{2}}{c^{2}}\text{ or }y\leq -\frac{18\sqrt{55}|c|+\frac{279c}{2}}{c^{2}}\right)\text{ and }y\neq 0\text{ and }c\neq 0\end{matrix}\right.$$