## The equation below is equivalent to which of the following quadratic equations? (1/(a+x))+(1/(b+x))=(1/(c+x)) a. ax

Question

The equation below is equivalent to which of the following quadratic equations?

(1/(a+x))+(1/(b+x))=(1/(c+x))

a. ax^2+bc+c=0
b. x^2+2cx+bc+ac-ab=0
c. 2x^2+(b+c-a)x+b(c+a)=0
d. (x^2/a^2)+(b^2/c^2)=((b+c)/(a+c))

an explanation would be appreciated! ðŸ™‚

in progress 0
2 weeks 2021-09-12T05:04:37+00:00 1 Answer 0

Â  b. Â x^2 +2cx +bc+ac-ab = 0

Step-by-step explanation:

It’s a matter of what I would describe as tedious algebra. You have to multiply by the least common denominator, then simplify to standard form.

After multiplying the equation by (x+a)(x+b)(x+c) and subtracting the right side, you have …

Â  (x +b)(x +c) +(x +a)(x +c) -(x +a)(x +b) = 0

Expanding each factor pair gives …

Â  (xÂ² +(b+c)x +bc) +(xÂ² +(a+c)x +ac) -(xÂ² +(a+b)x +ab) = 0

Collecting terms gives …

Â  xÂ²(1 +1 -1) +x(b+c +a+c -a -b) +(bc +ac -ab) = 0

Â  xÂ² +2cx +bc +ac -ab = 0 . . . . . matches selection B