Task 4—Solving Rational Equations

Using the equation below as a model, fill in numbers in the place of a and b to create a rational equation that has an extraneous solution.

x plus a over ax = b over x

Part 1. Show all work to solve for x in the equation and check the solution.

Part 2. Explain how to identify the extraneous solution and what it means.

Question

Task 4—Solving Rational Equations

Using the equation below as a model, fill in numbers in the place of a and b to create a rational equation that has an extraneous solution.

x plus a over ax = b over x

Part 1. Show all work to solve for x in the equation and check the solution.

Part 2. Explain how to identify the extraneous solution and what it means.

eliesaab · Answer

Is it
$$
\frac {x+a}{ a x}=b
$$

eliesaab · Answer

Multiply the two side by a x, to get
x+a = a b x
This should be easy from now on

eliesaab · Answer

Subtract abx from both sides
x-a bx + a=0

eliesaab · Answer

Add -a to both sides
x-abx =-a

eliesaab · Answer

You should be able to find x now

eliesaab · Answer

I will give you last step
x(1-ab)=-a

eliesaab · Answer

x=?