solve: a^2 / ( a - x ) + x^2 / ( x - a ) = 2 a?

Answer 1

Hi,

a²........x²
-----.+.---- = 2a
a-x.....x-a

Multiply the 2nd fraction by -1 on the top and bottom. This will give a common denominator on the fractions.

a²........-x²
-----.+.---- = 2a
a-x.....a-x

Now multiply by a-x to eliminate fractions.

a² - x² = 2a(a - x)

a² - x² = 2a² - 2ax

x² - 2ax + a² = 0

Factor and solve.

(x - a)(x - a) = 0

x = a

However, if x = a and this was substituted into the equation, the denominator would equal zero, so this answer must be discarded. Therefore there is NO SOLUTION!!

I hope that helps!! :-)

Answer 2

well what i would do is take a -1 out of the denominator of x^2/(x-a). when you do that you get x^2/-1(-x+a) you can rearrange it so that it looks like this: -x^2/(a-x) now the equation looks like this:
a^2/(a-x) - x^2/(a-x) = 2a now you have the same denominator so you can subtract the numerator.
you get: a^2-x^2/(a-x) = 2a/1 now you can cross-multiply by multiplying the numerator of the left side of the equation by the denominator on the right side and vice versa. you should get: a^2-x^2=2a(a-x)
you can factor the left side of the equation: (a-x)(a+x)
then divide by (a-x) and you have: a+x=2a
subtract a and you have a=x
This answer doesn't make sense so there is no solution.

Answer 3

Quit posting your homework on here man.