(x+3)/(x+8)-(x-8)/(x-3) I worked this out and got -55 Ans. But was marked wrong because the Ans. is 55 why and how does this end with no minus(-)sign please show working
(x+3)/(x+8)-(x-8)/(x-3)
=[(x+3)(x-3) - (x-8)(x+8)]/[(x+8)(x-3)]
=[(x^2-9)-(x^2-64)]/[(x+8)(x-3)]
= (-9+64)/[(x+8)(x-3)]
= 55/[(x+8)(x-3)]
You probably forgot to use parentheses to keep track of quantities. But aside from that, what did you do with your denominator?
hey i know the answer now i wrote left to right instead of right to left and botched
the answer
To evaluate the expression (x+3)/(x+8) - (x-8)/(x-3), we need to find a common denominator for the two fractions and then simplify the expression.
First, let's find the least common denominator (LCD) for the two fractions. The LCD will be the product of the denominators, (x+8) and (x-3). Therefore, the LCD is (x+8)(x-3).
Next, we need to apply the LCD to each fraction, so that the denominators become the same. To do this, we multiply the numerator and denominator of each fraction by factors that will make the denominators equal to the LCD.
For the first fraction, (x+3)/(x+8), we need to multiply both the numerator and denominator by (x-3) to obtain the common denominator. This gives us:
[(x+3)(x-3)]/[(x+8)(x-3)]
Expanding the numerator, we get: (x^2 - 9)
For the second fraction, (x-8)/(x-3), we need to multiply both the numerator and denominator by (x+8) to obtain the common denominator. This gives us:
[(x-8)(x+8)]/[(x+8)(x-3)]
Expanding the numerator, we get: (x^2 - 64)
Now, we can rewrite the expression with the common denominator:
[(x^2 - 9)]/[(x+8)(x-3)] - [(x^2 - 64)]/[(x+8)(x-3)]
To subtract fractions with the same denominator, we subtract the numerators while keeping the common denominator:
[(x^2 - 9) - (x^2 - 64)]/[(x+8)(x-3)]
Simplifying the numerator, we get:
[x^2 - 9 - x^2 + 64]/[(x+8)(x-3)]
Combining like terms in the numerator, we have:
[55]/[(x+8)(x-3)]
Now, the expression is simplified to 55/[(x+8)(x-3)].
As you can see, there is no negative sign in the final answer. It seems that you made an error when subtracting the numerators. The correct answer would indeed be 55.