Solve 9+x/6+6/9=x-2a/a

$$\frac { 9 + x } { 6 } + \frac { 6 } { 9 } = \frac { x - 2 a } { a }$$

Solve for a

$$a=\frac{6x}{x+25}$$

$$x\neq 0\text{ and }x\neq -25$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 18a, the least common multiple of 6,9,a.

$$3a\left(9+x\right)+2a\times 6=18\left(x-2a\right)$$

Use the distributive property to multiply 3a by 9+x.

$$27a+3ax+2a\times 6=18\left(x-2a\right)$$

Multiply 2 and 6 to get 12.

$$27a+3ax+12a=18\left(x-2a\right)$$

Combine 27a and 12a to get 39a.

$$39a+3ax=18\left(x-2a\right)$$

Use the distributive property to multiply 18 by x-2a.

$$39a+3ax=18x-36a$$

Add 36a to both sides.

$$39a+3ax+36a=18x$$

Combine 39a and 36a to get 75a.

$$75a+3ax=18x$$

Combine all terms containing a.

$$\left(75+3x\right)a=18x$$

The equation is in standard form.

$$\left(3x+75\right)a=18x$$

Divide both sides by 75+3x.

$$\frac{\left(3x+75\right)a}{3x+75}=\frac{18x}{3x+75}$$

Dividing by 75+3x undoes the multiplication by 75+3x.

$$a=\frac{18x}{3x+75}$$

Divide 18x by 75+3x.

$$a=\frac{6x}{x+25}$$

Variable a cannot be equal to 0.

$$a=\frac{6x}{x+25}\text{, }a\neq 0$$

Solve for x

$$x=-\frac{25a}{a-6}$$

$$a\neq 6\text{ and }a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 18a, the least common multiple of 6,9,a.

$$3a\left(9+x\right)+2a\times 6=18\left(x-2a\right)$$

Use the distributive property to multiply 3a by 9+x.

$$27a+3ax+2a\times 6=18\left(x-2a\right)$$

Multiply 2 and 6 to get 12.

$$27a+3ax+12a=18\left(x-2a\right)$$

Combine 27a and 12a to get 39a.

$$39a+3ax=18\left(x-2a\right)$$

Use the distributive property to multiply 18 by x-2a.

$$39a+3ax=18x-36a$$

Subtract 18x from both sides.

$$39a+3ax-18x=-36a$$

Subtract 39a from both sides.

$$3ax-18x=-36a-39a$$

Combine -36a and -39a to get -75a.

$$3ax-18x=-75a$$

Combine all terms containing x.

$$\left(3a-18\right)x=-75a$$

Divide both sides by 3a-18.

$$\frac{\left(3a-18\right)x}{3a-18}=-\frac{75a}{3a-18}$$

Dividing by 3a-18 undoes the multiplication by 3a-18.

$$x=-\frac{75a}{3a-18}$$

Divide -75a by 3a-18.

$$x=-\frac{25a}{a-6}$$