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.