Solving Rational Equations

In the equation $\frac{5}{2𝑥−4}+\frac{2}{𝑥+3}=\frac{3}{𝑥−2}$ , the factored form of the denominator  $2x-4$  is...

•  $2\left(x+2\right)$  

•  $2\left(x-2\right)$  

•  $\left(x+2\right)\left(x-2\right)$  

•  $\left(x-2\right)\left(x-2\right)$  

To solve the equation $\frac{5}{2\left(𝑥−2\right)}+\frac{2}{𝑥+3}=\frac{3}{𝑥−2}$ , we multiply both sides by the LCD which is...

•  $2\left(x-2\right)$  

•  $2\left(x+3\right)$  

•  $2\left(x+2\right)\left(x-3\right)$  

•  $2\left(x-2\right)\left(x+3\right)$  

After multiplying the equation $\frac{5}{2\left(𝑥−2\right)}+\frac{2}{𝑥+3}=\frac{3}{𝑥−2}$ by its LCD it will become...

•  $5\left(x-2\right)+2\left(2\right)\left(x+3\right)=2\left(3\right)\left(x-2\right)$  

•  $5\left(x+3\right)+2\left(2\right)\left(x-2\right)=2\left(3\right)\left(x+3\right)$  

•  $5\left(x-3\right)+2\left(2\right)\left(x+2\right)=2\left(3\right)\left(x-3\right)$  

•  $5\left(x+2\right)+2\left(2\right)\left(x-3\right)=2\left(3\right)\left(x+2\right)$  

After applying distributive property of multiplication to  $5\left(x+3\right)+2\left(2\right)\left(x-2\right)=2\left(3\right)\left(x+3\right)$ , it will become...

•  $5x+3+2x-2=3x+3$ 

•  $5x+15+4x-2=6x+3$ 

•  $5x+15+4x-2=6x+3$ 

•  $5x+15+4x-8=6x+18$ 

Which of the following will be the solution to rational the equation $\frac{5}{2𝑥−4}+\frac{2}{𝑥+3}=\frac{3}{𝑥−2}$ ?

•  $\frac{11}{3}$  

•  $\frac{3}{11}$  

•  $-\frac{11}{3}$  

•  $-\frac{3}{11}$