Solving rational equations.

Question: How do we solve rational equations?

When solving rational equation their are are a few steps that break down these otherwise complex equations.

Solve this rational equation:
x+2x−2=xx−2


Step 1:  Make the denominators the same by multiplying x-2 to the denominator and numerator of x. As shown below.
(x−2)x(x−2)+2(x−2)=x(x−2)

Step 2:  Cancel out all the denominators or cross out all of x-2.
(x−2)x+2=x

Step 3:  Distribute the multiplication or distribute (x-2)x.
x2−2x+2=x

Step 4: Combine like terms . Which in this equation their are none so just keep the equation the same.
x2−2x+2=x

Step 5: Set the equation equal to zero by subtracting x to the equation creating the equation below.
x2−3x+2=0

Step 6: Factor out the equation shown below.
(x−2)(x−1)=0
Step 7: Change the signs to its opposite.
x={2,1}

Step 8: Check these numbers by plugging them into the equation.

x=2?
(2)+2(2)−2=(2)(2)−2
2+20=20

number 2 will be rejected or not the answer because it divides by zero which makes it undefined.
 Now plug in 1

x=1?
(1)+2(1)−2=(1)(1)−2
1+2−1=1−1
−1=−1
Check
Final Answer:{1}

Now try it yourself:

x+x+7x+6=1x+6

Source: http://www.deltamath.com/student.html