This document discusses solving rational equations by multiplying each side of the equation by the common denominator to eliminate fractions. It provides 4 examples of solving rational equations: 1) 1/3 = 14/x, solved by cross multiplying to get x = 42 2) 3/(x+4) = 5/(x - 2), solved by multiplying both sides by (x+4)(x - 2) to get -13 = x 3) (x - 4)/4 + x/3 = 6, solved by multiplying both sides by 12 to get x = 12 4) 1/2 + 3/x = 3/4, solved by multiplying both sides by 4x to get x = 12.

1. Subtitle

2. An equation containing one or more rational
expressions is called a rational equation. Solving rational
equation is done by multiplying each side of the equation by
the common denominator to eliminate the fractions.

3. Example 1. Solve
1
3
=
14
𝑥
.
Solution Checking:
(1)(x) = (14)(3) Cross Multiplication
x = 42
Or Mul. by LCD
1
3
=
14
𝑥
=
(3𝑥)(1)
3
=
(3𝑥)14
𝑥
= (x)(1) = (3)(14)
x = 42
1
3
=
14
𝑥
=
1
3
=
14
42
(1) (42) = (14)(3)
42 = 42

4. Example 2. Solve
3
𝑥+4
=
5
𝑥 −2
Solution
3
𝑥+4
=
5
𝑥 −2
3(x – 2) = 5(x + 4)
3x – 6 = 5x + 20
-20 - 6 = 5x - 3x
-26 = 2x
-13 = x
Or
(𝑥+4)(𝑥 −2)(3)
𝑥+4
=
(𝑥+4)(𝑥 −2)(5)
𝑥 −2
(x – 2)(3) = (x + 4)(5)
3x – 6 = 5x + 20
3x – 5x = 20 + 6
-2x = 26
x = -13

5. Example 3. Solve
𝑥 − 4
4
+
𝑥
3
= 6
Solution Checking:
𝑥 − 4
4
+
𝑥
3
= 6
𝟑
12 (𝑥 − 4)
4
+
𝟒
12 (𝑥)
3
= 6 (12)
3(x – 4) + 4(x) = 72
3x – 12 + 4x = 72
3x + 4x = 72 + 12
7x = 84
x = 12
𝑥 − 4
4
+
𝑥
3
= 6
12 − 4
4
+
12
3
= 6
8
4
+ 4 = 6
2 + 4 = 6
6 = 6

6. Example 4. Solve for x in
1
2
+
3
𝑥
=
3
4
.
Solution Checking
1
2
+
3
𝑥
=
3
4
2
(4𝑥)(1)
2
+
(4𝑥)(3)
𝑥
=
(4𝑥)(3)
4
(2)(x)(1) + (4)(3) = (x)(3)
2x + 12 = 3x
12 = 3x – 2x
12 = x
1
2
+
3
𝑥
=
3
4
1
2
+
3
(12)
=
3
4
6+3
12
=
3
4
9
12
=
3
4
3
4
=
3
4

7. Thank
You