Solve 3T+9/6T+3=x+2/x-3

$$\frac { 3 T + 9 } { 6 T + 3 } = \frac { x + 2 } { x - 3 }$$

Solve for T

$$T=\frac{2x-11}{x+7}$$

$$x\neq 3\text{ and }x\neq -7$$

Steps for Solving Linear Equation

Variable T cannot be equal to -\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 3\left(x-3\right)\left(2T+1\right), the least common multiple of 6T+3,x-3.

$$\left(x-3\right)\left(3T+9\right)=\left(6T+3\right)\left(x+2\right)$$

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

$$3xT+9x-9T-27=\left(6T+3\right)\left(x+2\right)$$

Use the distributive property to multiply 6T+3 by x+2.

$$3xT+9x-9T-27=6Tx+12T+3x+6$$

Subtract 6Tx from both sides.

$$3xT+9x-9T-27-6Tx=12T+3x+6$$

Combine 3xT and -6Tx to get -3xT.

$$-3xT+9x-9T-27=12T+3x+6$$

Subtract 12T from both sides.

$$-3xT+9x-9T-27-12T=3x+6$$

Combine -9T and -12T to get -21T.

$$-3xT+9x-21T-27=3x+6$$

Subtract 9x from both sides.

$$-3xT-21T-27=3x+6-9x$$

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

$$-3xT-21T-27=-6x+6$$

Add 27 to both sides.

$$-3xT-21T=-6x+6+27$$

Add 6 and 27 to get 33.

$$-3xT-21T=-6x+33$$

Combine all terms containing T.

$$\left(-3x-21\right)T=-6x+33$$

The equation is in standard form.

$$\left(-3x-21\right)T=33-6x$$

Divide both sides by -3x-21.

$$\frac{\left(-3x-21\right)T}{-3x-21}=\frac{33-6x}{-3x-21}$$

Dividing by -3x-21 undoes the multiplication by -3x-21.

$$T=\frac{33-6x}{-3x-21}$$

Divide -6x+33 by -3x-21.

$$T=-\frac{11-2x}{x+7}$$

Variable T cannot be equal to -\frac{1}{2}.

$$T=-\frac{11-2x}{x+7}\text{, }T\neq -\frac{1}{2}$$

Solve for x

$$x=\frac{7T+11}{2-T}$$

$$T\neq -\frac{1}{2}\text{ and }T\neq 2$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by 3\left(x-3\right)\left(2T+1\right), the least common multiple of 6T+3,x-3.

$$\left(x-3\right)\left(3T+9\right)=\left(6T+3\right)\left(x+2\right)$$

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

$$3xT+9x-9T-27=\left(6T+3\right)\left(x+2\right)$$

Use the distributive property to multiply 6T+3 by x+2.

$$3xT+9x-9T-27=6Tx+12T+3x+6$$

Subtract 6Tx from both sides.

$$3xT+9x-9T-27-6Tx=12T+3x+6$$

Combine 3xT and -6Tx to get -3xT.

$$-3xT+9x-9T-27=12T+3x+6$$

Subtract 3x from both sides.

$$-3xT+9x-9T-27-3x=12T+6$$

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

$$-3xT+6x-9T-27=12T+6$$

Add 9T to both sides.

$$-3xT+6x-27=12T+6+9T$$

Combine 12T and 9T to get 21T.

$$-3xT+6x-27=21T+6$$

Add 27 to both sides.

$$-3xT+6x=21T+6+27$$

Add 6 and 27 to get 33.

$$-3xT+6x=21T+33$$

Combine all terms containing x.

$$\left(-3T+6\right)x=21T+33$$

The equation is in standard form.

$$\left(6-3T\right)x=21T+33$$

Divide both sides by -3T+6.

$$\frac{\left(6-3T\right)x}{6-3T}=\frac{21T+33}{6-3T}$$

Dividing by -3T+6 undoes the multiplication by -3T+6.

$$x=\frac{21T+33}{6-3T}$$

Divide 21T+33 by -3T+6.

$$x=\frac{7T+11}{2-T}$$

Variable x cannot be equal to 3.

$$x=\frac{7T+11}{2-T}\text{, }x\neq 3$$