x-8/x-9-x+1/x+9+x-17/x^2-81 =x^3-81x^2-7x-27/x^2.
Can some check this my answer and see if it corre4ct please.
you appear to have completely ignored the order of operation, you must use brackets to show the expression in its proper way.
I will assume you meant
(x-8)/(x-9) - (x+1)/(x+9) + (x-17)/(x^2-81)
did you notice that x^2-81 = (x+9)(x-9), so x^2-81 is the LCD
then
(x-8)/(x-9) - (x+1)/(x+9) + (x-17)/(x^2-81)
=[(x-8)(x+9) - (x+1)(x-9) + x-17]/(x^2-81)
= [x^2+x-72 - (x^2-8x-9) + x-17]/(x^2-81)
= [x^2+x-72-x^2+8x-9+x-17]/(x^2-81)
= (10x-80)/(x^2-81)
check my steps, I tend to make stupid mistakes when typing and working out these questions at the same time
Thanks Reiny this is my first time and the operations was not in brackets so I DID NOT KNOW
No problem,
may people have difficulty writing fractions in this format, it is hard to create them
if you write x-8/x+9
it really means x - 8/x + 9 according to BEDMAS
so it is necessary to use brackets.
To check if your answer is correct, we can simplify both sides of the given equation and see if they are equivalent.
Starting with the left side of the equation:
x - 8 / (x - 9) - x + 1 / (x + 9) + x - 17 / (x^2 - 81)
To simplify this expression, we need to find a common denominator for all the terms. The common denominator for the first two terms is (x - 9)(x + 9)(x^2 - 81), and for the third term, it is (x + 9)(x - 9).
Now, let's simplify each term using the common denominator:
(x - 8)(x + 9)(x^2 - 81) / (x - 9)(x + 9)(x^2 - 81) - (x - 9)(x + 9)(x^2 - 81) / (x - 9)(x + 9)(x^2 - 81) + (x - 17) / (x + 9)(x - 9)
Expanding the numerators:
(x^3 + x^2 - 81x - 8x - 72x - 648) - (x^3 - x^2 - 81x + 9x^2 - 81x^2 + 9x^3 - 81x - 810 + x - 17) + (x - 17)
Combining like terms:
x^3 + x^2 - 81x - 8x - 72x - 648 - x^3 + x^2 + 81x - 9x^2 + 81x^2 - 9x^3 + 81x + 810 - x + 17 + x - 17
Many terms cancel out, leaving us with:
-8x^3 + 9x^2 - 5
Now looking at the right side of the equation:
(x^3 - 81x^2 - 7x - 27) / x^2
Dividing the numerator by x^2:
(-8x^3 + 9x^2 - 5) / x^2
Now, we can compare the simplified left side (-8x^3 + 9x^2 - 5) with the right side (-8x^3 + 9x^2 - 5). Since they are equal, we can conclude that your answer is correct.