7-5 DAY 2 PROBLEM SOLVING using Rational Equations
ALGEBRA 2
Name _______________________________Per_____
1. WITHOUT solving the equation, what possible solutions
can you rule out? Meaning – that once you solve the
equation, if you got x to be equal to that number, it
would be an extraneous solution.
2. Solve each equation. Do not use a graphing calculator to do so. Check each solution. (Hint: State what x can’t be first. x ≠ ? )
a.
5x
=
10 − x
x2
x − 10
b.
3x + 2
= 2 −
x +1
c.
1
x −1
x+3
− 1
x
d.
3x
6
+
x +1
2x
=
=
2x + 3
x +1
7
x
e.
x−4
=
x
g.
x
1
−
=
x +1
x − 5x − 6
2
6
x − 3x
f.
2
2
x
+
=
x +1
x −1
2
x −1
2
2
x + 2x + 1
2
In Exercise 3, make a table, create an equation in order to solve each problem. Use WORK DONE = (WORK RATE) X (TIME).
SHOW ALL WORK.
3a. A pool has two drains. The largest can drain the pool in 6 hours, the smallest
can drain the pool in 10 hours. How long will it take to drain the pool if both
drains are open?
Work Rate
Largest
Smallest
Time
Work Done
b. Julian can mulch a garden in 20 minutes. Together Julian and his friend,
Sue, can mulch the same garden in 30 minutes.
How long would it take Sue to mulch that garden by herself?
Work Rate
Time
Work Done
Julian
Sue
4. Solve using your graphing calculator. Draw a quick sketch of what you see in your calculator. Round to the nearest tenth if necessary.
a.
x+4
x
=
x +1
2
b. x
=
−9
x
REVIEW
5. Simplify.
a.
2 x2 − 8
x2 − x − 6
b.
x − x2
x2 − 2 x + 1
6. Perform the following operations and simplify each answer.
a.
−3xy 9 5 x 6 y
⋅
10 x7 y 3 9 x 2 y8
b.
12mn12 3n3
÷ 2
m7
4m
7. Find the quotient.
x 2 + 9x − 22
÷ ( x − 2)
x 2 − 121
8. Find the product
6x 2 − 7x − 3 2x 2 − 3x
⋅
4x 2 − 12x + 9
3x 2
9. What is the simplified form of the following complex fraction?
x2 − 9
2x 2 + 2x
x+4
1
+ 2
6x
2x
10. Find the sum.
11. Find the difference.
x −1 2
+
x+3 x
x−2
3
−
x + 6x + 8 x + 4
2