IXL - Solve rational equations (Algebra 1 practice)

Solve for g.

g − 2

^–2

g + 7

There may be 1 or 2 solutions.

g = or g =

ref_doc_title.

Learn with an example

question

Solve for t.

t + 1

t − 8

There may be 1 or 2 solutions.

t = or t =

key idea

To solve a rational equation, first clear the fractions, by multiplying both sides by the denominators or by the lowest common denominator (LCD). Then solve for the variable.

solution

Solve for t.

t + 1

t − 8

Multiply both sides by (t + 1)(t − 8)

4[(t + 1)(t − 8)]

t + 1

10[(t + 1)(t − 8)]

t − 8

Multiply both sides by (t + 1)(t − 8)

Simplify

4(t − 8)

10(t + 1)

Simplify

Apply the distributive property

4t − 32

10t + 10

Apply the distributive property

Subtract 4t from both sides

^–32

6t + 10

Subtract 4t from both sides

Subtract 10 from both sides

^–42

Subtract 10 from both sides

Divide both sides by 6

^–7

Divide both sides by 6

Now check whether this is an extraneous solution. Plugging t = ^–7 into the first denominator, t + 1, yields ^–6. Plugging t = ^–7 into the second denominator, t − 8, yields ^–15. Since neither denominator is 0, which would be undefined, this is a valid solution.

The
solution
is
t
= ^–7
.

Looking for more? Try this:

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	06

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

C.12Solve linear equations with variables on both sides

GG.3Multiply and divide rational expressions

Z.3Solve a quadratic equation by factoring

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!