Simplify
f+ g/f-g when f(x)= x-2/x+5. And g(x)= x-5/x+2
Choices,
A. 2x^2 -29/21
B. 21/2x^2 -29
C. - 2x^2 -29 /29
D. - 29/2x^2-29
what's the trouble? Just plug in the values for f and g.
Assuming the usual carelessness with parentheses, we have
(f+g)/(f-g)
(x-2)/(x+5) + (x-5)/(x+2)
-----------------------------------
(x-2)/(x+5) - (x-5)/(x+2)
= (2x^2-29)/21
Thank you! I always mess up on these i had originally gotten B but i guess thats my error.
To simplify the expression, we need to substitute the given functions f(x) and g(x) into the expression f + g / f - g and then simplify the resulting expression.
First, let's substitute f(x) and g(x) into the expression:
f + g / f - g = (x-2/x+5) + (x-5/x+2) / (x-2/x+5) - (x-5/x+2)
Now let's simplify the numerator:
(x-2/x+5) + (x-5/x+2) = (x^2 - 2(x+5) + (x^2 - 5(x+2))) / (x+5)(x+2)
= (x^2 - 2x - 10 + x^2 - 5x -10) / (x+5)(x+2)
= (2x^2 - 7x - 20) / (x+5)(x+2)
And now let's simplify the denominator:
(x-2/x+5) - (x-5/x+2) = ((x(x+2) - 2(x+5)) - (x(x+5) - 5(x+2))) / (x+5)(x+2)
= (x^2 + 2x - 2x - 10 - (x^2 + 5x - 5x - 25)) / (x+5)(x+2)
= (-8) / (x+5)(x+2)
= -8 / (x+5)(x+2)
Now we can combine the numerator and the denominator:
(2x^2 - 7x - 20) / (x+5)(x+2) / (-8) / (x+5)(x+2)
To divide by a fraction, we can multiply by its reciprocal:
= (2x^2 - 7x - 20) / (x+5)(x+2) * (-8) * (x+5)(x+2)
Now we can simplify the expression:
= (-8)(2x^2 - 7x - 20) / (x+5)(x+2)
= -16x^2 + 56x + 160 / (x+5)(x+2)
Therefore, the simplified expression is -16x^2 + 56x + 160 / (x+5)(x+2).
None of the given choices match this simplified expression, so the correct answer is not listed.