Solve x/a+x/b=dx/-3+3

$$\frac { x } { a } + \frac { x } { b } = \frac { d x } { - 3 } + 3$$

Solve for a

$$a=-\frac{3bx}{bdx+3x-9b}$$

$$\left(b\neq 0\text{ and }x\neq 0\text{ and }x\neq \frac{9b}{bd+3}\text{ and }x\neq 3b\right)\text{ or }\left(b\neq 0\text{ and }x\neq 0\text{ and }x\neq \frac{9b}{bd+3}\text{ and }d\neq 0\right)\text{ or }\left(x\neq 0\text{ and }b=-\frac{3}{d}\text{ and }d\neq 0\right)$$

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 3ab, the least common multiple of a,b,-3.

$$3bx+3ax=-abdx+3ab\times 3$$

Multiply 3 and 3 to get 9.

$$3bx+3ax=-abdx+9ab$$

Add abdx to both sides.

$$3bx+3ax+abdx=9ab$$

Subtract 9ab from both sides.

$$3bx+3ax+abdx-9ab=0$$

Subtract 3bx from both sides. Anything subtracted from zero gives its negation.

$$3ax+abdx-9ab=-3bx$$

Combine all terms containing a.

$$\left(3x+bdx-9b\right)a=-3bx$$

The equation is in standard form.

$$\left(bdx+3x-9b\right)a=-3bx$$

Divide both sides by 3x+bdx-9b.

$$\frac{\left(bdx+3x-9b\right)a}{bdx+3x-9b}=-\frac{3bx}{bdx+3x-9b}$$

Dividing by 3x+bdx-9b undoes the multiplication by 3x+bdx-9b.

$$a=-\frac{3bx}{bdx+3x-9b}$$

Variable a cannot be equal to 0.

$$a=-\frac{3bx}{bdx+3x-9b}\text{, }a\neq 0$$

Solve for b

$$b=-\frac{3ax}{adx+3x-9a}$$

$$\left(a\neq 0\text{ and }x\neq 0\text{ and }x\neq \frac{9a}{ad+3}\text{ and }x\neq 3a\right)\text{ or }\left(a\neq 0\text{ and }x\neq 0\text{ and }x\neq \frac{9a}{ad+3}\text{ and }d\neq 0\right)\text{ or }\left(x\neq 0\text{ and }a=-\frac{3}{d}\text{ and }d\neq 0\right)$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3ab, the least common multiple of a,b,-3.

$$3bx+3ax=-abdx+3ab\times 3$$

Multiply 3 and 3 to get 9.

$$3bx+3ax=-abdx+9ab$$

Add abdx to both sides.

$$3bx+3ax+abdx=9ab$$

Subtract 9ab from both sides.

$$3bx+3ax+abdx-9ab=0$$

Subtract 3ax from both sides. Anything subtracted from zero gives its negation.

$$3bx+abdx-9ab=-3ax$$

Combine all terms containing b.

$$\left(3x+adx-9a\right)b=-3ax$$

The equation is in standard form.

$$\left(adx+3x-9a\right)b=-3ax$$

Divide both sides by 3x+adx-9a.

$$\frac{\left(adx+3x-9a\right)b}{adx+3x-9a}=-\frac{3ax}{adx+3x-9a}$$

Dividing by 3x+adx-9a undoes the multiplication by 3x+adx-9a.

$$b=-\frac{3ax}{adx+3x-9a}$$

Variable b cannot be equal to 0.

$$b=-\frac{3ax}{adx+3x-9a}\text{, }b\neq 0$$