Question

Which expression is equivalent to x/(x-4)(x-5)+1/(x-5)

Answer 1

Evaluate

(
`x^(3) -10x^(2) + 26x-4 \\ (x-5) (x-4)`

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

​

​