Solve 2x+4/b-3a+ab-3-b+9/b^2-9=x+2/b+3+ab+3a

$$\frac { 2 x + 4 } { b - 3 a + a b - 3 } - \frac { b + 9 } { b ^ { 2 } - 9 } = \frac { x + 2 } { b + 3 + a b + 3 a }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=x+1\text{, }&x\neq -2\text{ and }b\neq -3\text{ and }b\neq 3\\a\neq -1\text{, }&b=-9\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by \left(b-3\right)\left(a+1\right)\left(b+3\right), the least common multiple of b-3a+ab-3,b^{2}-9,b+3+ab+3a.

$$\left(b+3\right)\left(2x+4\right)-\left(a+1\right)\left(b+9\right)=\left(b-3\right)\left(x+2\right)$$

Use the distributive property to multiply b+3 by 2x+4.

$$2bx+4b+6x+12-\left(a+1\right)\left(b+9\right)=\left(b-3\right)\left(x+2\right)$$

Use the distributive property to multiply a+1 by b+9.

$$2bx+4b+6x+12-\left(ab+9a+b+9\right)=\left(b-3\right)\left(x+2\right)$$

To find the opposite of ab+9a+b+9, find the opposite of each term.

$$2bx+4b+6x+12-ab-9a-b-9=\left(b-3\right)\left(x+2\right)$$

Combine 4b and -b to get 3b.

$$2bx+3b+6x+12-ab-9a-9=\left(b-3\right)\left(x+2\right)$$

Subtract 9 from 12 to get 3.

$$2bx+3b+6x+3-ab-9a=\left(b-3\right)\left(x+2\right)$$

Use the distributive property to multiply b-3 by x+2.

$$2bx+3b+6x+3-ab-9a=bx+2b-3x-6$$

Subtract 2bx from both sides.

$$3b+6x+3-ab-9a=bx+2b-3x-6-2bx$$

Combine bx and -2bx to get -bx.

$$3b+6x+3-ab-9a=-bx+2b-3x-6$$

Subtract 3b from both sides.

$$6x+3-ab-9a=-bx+2b-3x-6-3b$$

Combine 2b and -3b to get -b.

$$6x+3-ab-9a=-bx-b-3x-6$$

Subtract 6x from both sides.

$$3-ab-9a=-bx-b-3x-6-6x$$

Combine -3x and -6x to get -9x.

$$3-ab-9a=-bx-b-9x-6$$

Subtract 3 from both sides.

$$-ab-9a=-bx-b-9x-6-3$$

Subtract 3 from -6 to get -9.

$$-ab-9a=-bx-b-9x-9$$

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by -b-9.

$$\frac{\left(-b-9\right)a}{-b-9}=-\frac{\left(b+9\right)\left(x+1\right)}{-b-9}$$

Dividing by -b-9 undoes the multiplication by -b-9.

$$a=-\frac{\left(b+9\right)\left(x+1\right)}{-b-9}$$

Divide -\left(1+x\right)\left(9+b\right) by -b-9.

$$a=x+1$$

Variable a cannot be equal to -1.

$$a=x+1\text{, }a\neq -1$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-9\text{, }&a\neq -1\\b\in \mathrm{C}\setminus -3,3\text{, }&x=a-1\text{ and }a\neq -1\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable b cannot be equal to any of the values -3,3 since division by zero is not defined. Multiply both sides of the equation by \left(b-3\right)\left(a+1\right)\left(b+3\right), the least common multiple of b-3a+ab-3,b^{2}-9,b+3+ab+3a.

$$\left(b+3\right)\left(2x+4\right)-\left(a+1\right)\left(b+9\right)=\left(b-3\right)\left(x+2\right)$$

Use the distributive property to multiply b+3 by 2x+4.

$$2bx+4b+6x+12-\left(a+1\right)\left(b+9\right)=\left(b-3\right)\left(x+2\right)$$

Use the distributive property to multiply a+1 by b+9.

$$2bx+4b+6x+12-\left(ab+9a+b+9\right)=\left(b-3\right)\left(x+2\right)$$

To find the opposite of ab+9a+b+9, find the opposite of each term.

$$2bx+4b+6x+12-ab-9a-b-9=\left(b-3\right)\left(x+2\right)$$

Combine 4b and -b to get 3b.

$$2bx+3b+6x+12-ab-9a-9=\left(b-3\right)\left(x+2\right)$$

Subtract 9 from 12 to get 3.

$$2bx+3b+6x+3-ab-9a=\left(b-3\right)\left(x+2\right)$$

Use the distributive property to multiply b-3 by x+2.

$$2bx+3b+6x+3-ab-9a=bx+2b-3x-6$$

Subtract bx from both sides.

$$2bx+3b+6x+3-ab-9a-bx=2b-3x-6$$

Combine 2bx and -bx to get bx.

$$bx+3b+6x+3-ab-9a=2b-3x-6$$

Subtract 2b from both sides.

$$bx+3b+6x+3-ab-9a-2b=-3x-6$$

Combine 3b and -2b to get b.

$$bx+b+6x+3-ab-9a=-3x-6$$

Subtract 6x from both sides.

$$bx+b+3-ab-9a=-3x-6-6x$$

Combine -3x and -6x to get -9x.

$$bx+b+3-ab-9a=-9x-6$$

Subtract 3 from both sides.

$$bx+b-ab-9a=-9x-6-3$$

Subtract 3 from -6 to get -9.

$$bx+b-ab-9a=-9x-9$$

Add 9a to both sides.

$$bx+b-ab=-9x-9+9a$$

Combine all terms containing b.

$$\left(x+1-a\right)b=-9x-9+9a$$

The equation is in standard form.

$$\left(x-a+1\right)b=-9x+9a-9$$

Divide both sides by 1+x-a.

$$\frac{\left(x-a+1\right)b}{x-a+1}=\frac{-9x+9a-9}{x-a+1}$$

Dividing by 1+x-a undoes the multiplication by 1+x-a.

$$b=\frac{-9x+9a-9}{x-a+1}$$

Divide -9-9x+9a by 1+x-a.

$$b=-9$$

Solve for a

$$\left\{\begin{matrix}a=x+1\text{, }&x\neq -2\text{ and }|b|\neq 3\\a\neq -1\text{, }&b=-9\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by \left(b-3\right)\left(a+1\right)\left(b+3\right), the least common multiple of b-3a+ab-3,b^{2}-9,b+3+ab+3a.

$$\left(b+3\right)\left(2x+4\right)-\left(a+1\right)\left(b+9\right)=\left(b-3\right)\left(x+2\right)$$

Use the distributive property to multiply b+3 by 2x+4.

$$2bx+4b+6x+12-\left(a+1\right)\left(b+9\right)=\left(b-3\right)\left(x+2\right)$$

Use the distributive property to multiply a+1 by b+9.

$$2bx+4b+6x+12-\left(ab+9a+b+9\right)=\left(b-3\right)\left(x+2\right)$$

To find the opposite of ab+9a+b+9, find the opposite of each term.

$$2bx+4b+6x+12-ab-9a-b-9=\left(b-3\right)\left(x+2\right)$$

Combine 4b and -b to get 3b.

$$2bx+3b+6x+12-ab-9a-9=\left(b-3\right)\left(x+2\right)$$

Subtract 9 from 12 to get 3.

$$2bx+3b+6x+3-ab-9a=\left(b-3\right)\left(x+2\right)$$

Use the distributive property to multiply b-3 by x+2.

$$2bx+3b+6x+3-ab-9a=bx+2b-3x-6$$

Subtract 2bx from both sides.

$$3b+6x+3-ab-9a=bx+2b-3x-6-2bx$$

Combine bx and -2bx to get -bx.

$$3b+6x+3-ab-9a=-bx+2b-3x-6$$

Subtract 3b from both sides.

$$6x+3-ab-9a=-bx+2b-3x-6-3b$$

Combine 2b and -3b to get -b.

$$6x+3-ab-9a=-bx-b-3x-6$$

Subtract 6x from both sides.

$$3-ab-9a=-bx-b-3x-6-6x$$

Combine -3x and -6x to get -9x.

$$3-ab-9a=-bx-b-9x-6$$

Subtract 3 from both sides.

$$-ab-9a=-bx-b-9x-6-3$$

Subtract 3 from -6 to get -9.

$$-ab-9a=-bx-b-9x-9$$

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by -b-9.

$$\frac{\left(-b-9\right)a}{-b-9}=-\frac{\left(b+9\right)\left(x+1\right)}{-b-9}$$

Dividing by -b-9 undoes the multiplication by -b-9.

$$a=-\frac{\left(b+9\right)\left(x+1\right)}{-b-9}$$

Divide -\left(1+x\right)\left(9+b\right) by -b-9.

$$a=x+1$$

Variable a cannot be equal to -1.

$$a=x+1\text{, }a\neq -1$$

Solve for b

$$\left\{\begin{matrix}b=-9\text{, }&a\neq -1\\b\in \mathrm{R}\setminus 3,-3\text{, }&x=a-1\text{ and }a\neq -1\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable b cannot be equal to any of the values -3,3 since division by zero is not defined. Multiply both sides of the equation by \left(b-3\right)\left(a+1\right)\left(b+3\right), the least common multiple of b-3a+ab-3,b^{2}-9,b+3+ab+3a.

$$\left(b+3\right)\left(2x+4\right)-\left(a+1\right)\left(b+9\right)=\left(b-3\right)\left(x+2\right)$$

Use the distributive property to multiply b+3 by 2x+4.

$$2bx+4b+6x+12-\left(a+1\right)\left(b+9\right)=\left(b-3\right)\left(x+2\right)$$

Use the distributive property to multiply a+1 by b+9.

$$2bx+4b+6x+12-\left(ab+9a+b+9\right)=\left(b-3\right)\left(x+2\right)$$

To find the opposite of ab+9a+b+9, find the opposite of each term.

$$2bx+4b+6x+12-ab-9a-b-9=\left(b-3\right)\left(x+2\right)$$

Combine 4b and -b to get 3b.

$$2bx+3b+6x+12-ab-9a-9=\left(b-3\right)\left(x+2\right)$$

Subtract 9 from 12 to get 3.

$$2bx+3b+6x+3-ab-9a=\left(b-3\right)\left(x+2\right)$$

Use the distributive property to multiply b-3 by x+2.

$$2bx+3b+6x+3-ab-9a=bx+2b-3x-6$$

Subtract bx from both sides.

$$2bx+3b+6x+3-ab-9a-bx=2b-3x-6$$

Combine 2bx and -bx to get bx.

$$bx+3b+6x+3-ab-9a=2b-3x-6$$

Subtract 2b from both sides.

$$bx+3b+6x+3-ab-9a-2b=-3x-6$$

Combine 3b and -2b to get b.

$$bx+b+6x+3-ab-9a=-3x-6$$

Subtract 6x from both sides.

$$bx+b+3-ab-9a=-3x-6-6x$$

Combine -3x and -6x to get -9x.

$$bx+b+3-ab-9a=-9x-6$$

Subtract 3 from both sides.

$$bx+b-ab-9a=-9x-6-3$$

Subtract 3 from -6 to get -9.

$$bx+b-ab-9a=-9x-9$$

Add 9a to both sides.

$$bx+b-ab=-9x-9+9a$$

Combine all terms containing b.

$$\left(x+1-a\right)b=-9x-9+9a$$

The equation is in standard form.

$$\left(x-a+1\right)b=-9x+9a-9$$

Divide both sides by 1+x-a.

$$\frac{\left(x-a+1\right)b}{x-a+1}=\frac{-9x+9a-9}{x-a+1}$$

Dividing by 1+x-a undoes the multiplication by 1+x-a.

$$b=\frac{-9x+9a-9}{x-a+1}$$

Divide -9-9x+9a by 1+x-a.

$$b=-9$$