T10 Review

Reorder the following steps for solving rational equations.

• Solve and check for extraneous solutions

• Identify domain restrictions

• Rewrite all terms with denominators

• Remove Denominators (if CD type)

• Cross Multiply/ Multiply

What does domain restriction mean?

Answer explanation

Domain restriction refers to limiting the input values of a function to a specific subset of its original domain, ensuring that the function only operates on valid inputs.

• x=2

• x=1

• x=-10
• no solution

Answer explanation

You get x=-10, but in context the answer can't be negative

Match each rational equation with its domain restriction.

The value of r that satisfies the equation is (a)   .

• r= 5
• r= - 5, 4

• r= - 5

• r= 5, 4

The common denominator (CD) is (a)  

• x-2

• x+2

• (x+2)(x-2)

Answer explanation

The common denominator for the expressions involving (x+2) and (x-2) is their product, (x+2)(x-2). This is because it allows both expressions to be expressed with a single denominator, making it the correct choice.

• x = 2

• No Solution

• x = -10

• x = 10

Answer explanation

You get x=-10, but you can't have a negative answer in context

• No Solution

• y = -7

  y= 0.63

• y = -0.36

• y = 7.13

  y= -0.63

• y=7.13

Answer explanation

In context, you can't get a negative answer so -0.63 is not valid

• No Solution

• z = 2

• z = 1

• z = -5

• z=-8