OTCQ

Simplify

x3 * x4 ÷ x7 =

Aim 2-4 How do we add/subtract

Rational Expressions With

Like Denominators?Hwk: read 2-4 and do

problems 1-10 on page 75

Objectives - SWBAT add/subtract Rational Expressions With Like Denominators

Hwk: read 2-4 and do problems 1-10 on page 75

What conditions need to be met before two fractions can be added or subtracted?

Fractions must have the same denominator before they can be added or subtracted.

You can add and subtract rational expressions with like denominators in the same way. Add the numerators and write the sum over a common

denominator. Answers should always be expressed in simplest form.

7x x12 12

The common denominator is 12.

7x x12

Add the numerators.

8x12

Divide by the common factor of 4.

2

3

2x3

Simplified answer

w 6 w 39 9

w 6 w 39

2w 99

Add the numerators.

Any common factors to be divided?

No! The 9 in the numerator is a

TERM. Terms can’t be cancelled; only factors can be

cancelled!

The rational expression is in simplest form.

The common denominator is 9.

Sometimes the denominators of rational expressions are binomials. As long as each rational expression

has exactly the same binomial denominator, the process of addition is the same.

23y y3 y 3 y

The common denominator is 3 + y.

23y y3 y

Factor the numerator.

y 3 y

3 y

Divide by the common binomial factor.

y

15x 333x 9 33x 9

15x 333x 9

3 5x 1

3 11x 3

The common denominator is 33x + 9.

Add the numerators.

Divide by the common factor of 3.

Simplified answer5x 111x 3

Opposite Sign Denominators

m9m4

9mm2

Rewrite in good form with variable first.9m

m49m

m2

9mm4

9mm2

2m 4mm 9 m 9

9mm4m2

9mm2

Factor out -1 from the denominator.

Subtraction is the same as adding the opposite.

Subtract.

Negative monomial in numerator-- bring the negative sign out front of the rational expression.

2mm 9

The denominator

s are opposite binomials

(also known as inverse

denominators).

30x 56x 1 1 6x

Rewrite in good form with variable first.

30x 56x 1 6x 1

30x 5

6x 1 6x 1

30x 56x 1 6x 1

30x 56x 1

5(6x 1)6x 1

Factor out -1 from the denominator.

Subtracting a negative is the same as addition.

Add.

Factor the numerator to determine if there are common factors to be divided out.

The denominator

s are opposite binomials

(also known as inverse

denominators).

When subtracting rational expressions with like denominators, place the subtracted

quantity in parentheses. Then distribute the negative.

r 2 r 53 3

r 2 r 5

3

r 2 r 53

73

6a 4 4a 62a 2 2a 2

6a 4 4a 6

2a 2

2a 22a 2

6a 4 4a 62a 2

1

5x7x2

x33

5x7x2

x122

2

1 x 3 3x

2x 7x 5

2

1 x 3 3x

2x 7x 5

Put the subtracted quantity in parentheses. Distribute the negative.

2

2x 2

2x 7x 5

Factor the numerator and the denominator. X-box is necessary in the denominator.

2 x 1

x 1 2x 5

Divide out common factors.

22x 5

5x9x2

3x2

5x9x2

x2x422

2

5x9x2

3x2x2x42

2

5x9x2

3x2x2x42

2

5x9x2

3x4x42

2

1x25x

1x23x2

2x 3x 5

Put the subtracted quantity in parentheses. Distribute the negative.

Factor the numerator and denominator—remember to do the X-box.

Divide out common factors.

Aim 2-4 How do we add/subtract

Rational Expressions With

Like Denominators?Hwk: read 2-4 and do

problems 1-10 on page 75