Easy Algebra Step-by-Step

142 Easy Algebra Step-by-Step

3

31

x

x

x

≠ +x. 3 is a factor of the

numerator, but it is a term of the

denominator. It is a mistake to divide

out a term.

d.

3

3

x

+x

Step 1. Determine the GCF for 3x and 3 + x.

GCF = 1, so

3

3

x

+x

cannot be reduced

further.

e.^26

(^256)
x
xx^2 + 555
Step 1. Factor the numerator and denominator polynomials completely.
26
56

2

2

x

xx+ 555

=

()x 3

()x+ 22 ()x 3

Step 2. Determine the GCF for 2(x+ 3) and (x+ 2) (x+ 3).

GCF = (x+ 3)

Step 3. Use the fundamental principle to reduce the fraction.

(^22)
x 2
()()xx 33
()x+ 22 ()()xx 33

=

+

f. x

xx

2

2

1

21

−

+ 2 xx

Step 1. Factor the numerator and denominator polynomials completely.

x

xx

2

2 2

1

21 x

−

+ 2 x

=

()x+ 1 ()xx 1

()x+ 1

Step 2. Determine the GCF for (x + 1)(x − 1) and (x + 1)^2.

GCF = (x + 1)

Step 3. Write the numerator and denominator as equivalent products with

the GCF as one of the factors.

x

xx

2

2

1

21 x

−

+ 2 x

=

()x+^1 ()xx^1

()x+ 1 ()xx 1

26

6

2

(^22565)
x
xx^25
x
555 xx^25
≠

. 6 is a common
term in the numerator and denominator,
not a factor. Only divide out factors.