How do you combine #(x-10)/(x-8)-(x+10)/(8-x)#?

Answer 1

See the entire solution process below:

First, we need to put the fractions over common denominators. We can do this by multiplying the first fraction by the appropriate form of #1#:
#((-1)/-1 xx (x - 10)/(x - 8)) - (x + 10)/(8 - x) ->#
#((-1 xx (x - 10))/(-1 xx (x - 8))) - (x + 10)/(8 - x) ->#
#(-x + 10)/(-x + 8) - (x + 10)/(8 - x) ->#
#(-x + 10)/(8 - x) - (x + 10)/(8 - x)#

Now that there is a common denominator for each fraction we can subtract the numerators:

#(-x + 10 - x - 10)/(8 - x)#
#(-x - x + 10 - 10)/(8 - x)#
#(-2x + 0)/(8 - x)#
#(-2x)/(8 - x)#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To combine the expressions (x-10)/(x-8) and (x+10)/(8-x), we need to find a common denominator. In this case, the common denominator is (x-8)(8-x).

Next, we can rewrite the fractions with the common denominator:

(x-10)/(x-8) = (x-10)(-1)/((x-8)(-1)) = (-x+10)/(8-x)

(x+10)/(8-x) = -(x+10)/(x-8)

Now, we can combine the fractions by subtracting them:

(-x+10)/(8-x) - (-(x+10)/(x-8))

To subtract the fractions, we need to find a common denominator again, which is (x-8)(8-x).

(-x+10)/(8-x) - (-(x+10)/(x-8)) = ((-x+10)(x-8) - (-(x+10)(8-x)))/((x-8)(8-x))

Simplifying the numerator:

((-x+10)(x-8) - (-(x+10)(8-x))) = (-x^2 + 8x + 10x - 80 + x^2 + 10x - 8x + 80)/((x-8)(8-x))

Combining like terms:

(-x^2 + x^2 + 8x - 8x + 10x + 10x - 80 + 80)/((x-8)(8-x))

Simplifying further:

(20x)/((x-8)(8-x))

Therefore, the combined expression is (20x)/((x-8)(8-x)).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7