How do you simplify [x2−xx+5]⋅[x2+5x+4x4−x2]?
Answers
Answered by
0
Answer:
x
+
1
x
−
4
,
if
x
+
4
≠
0
Explanation:
Step 1: Factor both the numerator and denominator.
x
2
+
5
x
+
4
x
2
−
16
=
(
x
+
1
)
(
x
+
4
)
(
x
−
4
)
(
x
+
4
)
Step 2: Cancel common factors.
(
x
+
1
)
(
x
+
4
)
(
x
−
4
)
(
x
+
4
)
=
x
+
1
x
−
4
,
if
x
+
4
≠
0
Why write this "if
x
+
4
≠
0
" part? Because in the original quotient, if
x
+
4
=
0
(that is, if
x
=
–
4
), then the denominator would equal zero, and division by zero is undefined.
On its own,
x
+
1
x
−
4
does not give the same problem when
x
=
–
4
.
Since we want our simplified expression to reflect the original one in its entirety, we make sure it has all the same restrictions, including
x
+
4
≠
0
.
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