Equations with Rational Expressions


Multiply throughout by the LCD of all the
involved fractions.
Check your answer!
◦ We cannot divide by 0 and thus have to
exclude any values that result in zero
denominators.
Without actually solving, list all possible
numbers that would be rejected as
solutions.
5
8
𝑥
−
=
6𝑥 2𝑥 4
Without actually solving, list all possible
numbers that would be rejected as
solutions.
3
1
2
−
=
𝑥2 + 𝑥 𝑥 + 5 𝑥 − 7
Solve.
3
5 7
=
−
4𝑥 2𝑥 4
Solve.
𝑥 12
−
=1
2 𝑥
Solve.
3𝑥 + 1 6𝑥 + 5
=
𝑥−4
2𝑥 − 7
Solve.
6
5
−20
+ = 2
𝑥 − 4 𝑥 𝑥 − 4𝑥
Solve.
1
3
5
+
= 2
𝑦 + 2 𝑦 + 7 𝑦 + 9𝑦 + 14
Solve.
2
4𝑥 − 7
−2𝑥 + 5𝑥 − 4 𝑥 + 1
=
+
2
2
4𝑥 − 9
4𝑥 − 9
2𝑥 + 3
Applications of Rational Expressions
a.
b.
Solve for
Solve for
𝑔.
𝑎.
𝐴 = 𝑔𝑠
J
𝑞=
𝑎
Find 𝐿 if 𝑐 = 80 and 𝑏 = 7.
100𝑏
𝑐=
𝐿
Solve for
𝑚.
𝑘𝑀𝑚
𝐹=− 2
𝑟
Solve for z.
1 1 1
= +
𝐴 𝑣 𝑧
Solve for
𝑓.
𝑞𝑓
𝑚=
𝑓 + 𝑞𝑠
Solve for 𝑠.
1
𝐴 = ℎ(𝑠 + 𝑏)
3
Solve for
𝑥.
𝐹 𝑅+𝑥
=
𝑔
𝑥
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