Please follow the directions. 8 questions that are about Radical and Rational Expressions.
Directions: Please complete the following problems to the best of your ability. Make
sure to show as much work possible to support your answers. Problems with little to no
work shown will result in minimum credit earned.
1. Solve the radical equation. Make sure to check for extraneous solutions.
√2𝑥 − 1 − 𝑥 + 2 = 0
2. Find the restricted domain for the rational expression listed below. Remember you cannot
divide by zero.
3𝑥 − 1
𝑥2 − 9
3. Simplify the rational expression listed below. Factoring helps.
𝑥 3 − 𝑥 2 − 42𝑥
2𝑥 2 − 20𝑥 + 42
4. Multiply the two rational expressions listed below. Make sure your answer is as
simplified as possible.
𝑥2 − 9
4𝑥 2 − 25
∙
2𝑥 2 − 𝑥 − 10 𝑥 2 + 4𝑥 − 21
5. Simplify the complex fraction below. Make sure your answer is as simplified as
possible.
𝑥2
𝑥−1
3𝑥 2
𝑥+4
6. Subtract the two rational expressions listed below. Make sure your answer is as
simplified as possible.
3𝑥 + 9
2𝑥 − 2
−
𝑥 2 + 5𝑥 + 6 𝑥 2 + 𝑥 − 2
7. Add the two rational expressions listed below. Make sure your answer is as simplified as
possible.
3
𝑚
+ 2
𝑚 + 5 𝑚 + 7𝑚 + 10
8. Solve the rational equation below. Make sure you check and identify any extraneous
solution(s). Make sure to show your work.
1
1
𝑥−2
+
=
𝑥 𝑥−3
𝑥−3
Extra credit: ALL WORK MUST BE SHOWN TO EARN EXTRA CREDIT.
x−1
x+4
1
+
=
2
x − 2 2x + 1
2x − 3x − 2
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