Which expression is equivalent to x/(x-4)(x-5)+1/(x-5)
1 answer:
Answer:
Evaluate
(
Step-by-step explanation:
x/(x−4)(x−5)+1/(x−5)
Express
x−4
x
(x−5) as a single fraction.
x−4
x(x−5)
+
x−5
1
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x−4 and x−5 is (x−5)(x−4). Multiply
x−4
x(x−5)
times
x−5
x−5
. Multiply
x−5
1
times
x−4
x−4
.
(x−5)(x−4)
x(x−5)(x−5)
+
(x−5)(x−4)
x−4
Since
(x−5)(x−4)
x(x−5)(x−5)
and
(x−5)(x−4)
x−4
have the same denominator, add them by adding their numerators.
(x−5)(x−4)
x(x−5)(x−5)+x−4
Do the multiplications in x(x−5)(x−5)+x−4.
(x−5)(x−4)
x
3
−5x
2
−5x
2
+25x+x−4
Combine like terms in x
3
−5x
2
−5x
2
+25x+x−4.
(x−5)(x−4)
26x−4−10x
2
+x
3
Expand (x−5)(x−4).
x 2−9
x+20
26x−4−10x
2 +x 3
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