Subtract rational expressions $$ \frac{8 x+2}{3 x-3}-\frac{5 x+5}{3 x-3} $$

Question

UpStudy AI · Accepted Answer

Since both rational expressions have the same denominator, you can subtract them by subtracting the numerators:

Step 1. Write the difference over the common denominator:
  (8x + 2) / (3x - 3) - (5x + 5) / (3x - 3)
  = [ (8x + 2) - (5x + 5) ] / (3x - 3)

Step 2. Simplify the numerator:
  (8x + 2) - (5x + 5)
  = 8x + 2 - 5x - 5
  = (8x - 5x) + (2 - 5)
  = 3x - 3

Step 3. Notice that the numerator and the denominator are the same:
  (3x - 3) / (3x - 3)

For all values of x where the denominator is not zero, this simplifies to 1.

Step 4. Determine the domain restriction:
The denominator 3x - 3 equals zero when 3x - 3 = 0 → x = 1.
So, x cannot be 1.

Final Answer:
  The simplified expression is 1, for x ≠ 1.
The simplified expression is 1, provided that $$ x $$ is not equal to 1.

Subtract rational expressions \( \frac{8 x+2}{3 x-3}-\frac{5 x+5}{3 x-3} \)