Solve for x1-a-b-x-1-a-1-b-1-x- a-b-0

1/a+b+x 1/x = 1/a+1/b x a b x/x^2+(a+b)x=a+b/ab (a b)/x^2+(a+b)x=a+b/ab 1/x^2+(a+b)x=1/ab ab=x^2+(a+b)x ⇒ x^2+(a+b)x+ab=0 ⇒ x^2+ax+bx+ab=0 ⇒ x(x+a)+b(x+a)=0 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VII

Mathematics

Expression Formation

Solve for x1/...

Question

Solve for x
$\frac{1}{a + b + x} = \frac{1}{a} + \frac{1}{b} + \frac{1}{x}, a + b \neq 0$

Open in App

Solution

$\frac{1}{a + b + x} - \frac{1}{x} = \frac{1}{a} + \frac{1}{b} \frac{x - a - b - x}{x^{2} + (a + b) x} = \frac{a + b}{a b} \frac{- (a - b)}{x^{2} + (a + b) x} = \frac{a + b}{a b} \frac{- 1}{x^{2} + (a + b) x} = \frac{1}{a b} - a b = x^{2} + (a + b) x \Rightarrow x^{2} + (a + b) x + a b = 0 \Rightarrow x^{2} + a x + b x + a b = 0 \Rightarrow x (x + a) + b (x + a) = 0 \Rightarrow (x + b) (x + a) = 0 \Rightarrow x = - b, - a$

Suggest Corrections

Similar questions

Q. Solve for

x : \frac{1}{(a + b + x)} = \frac{1}{a} + \frac{1}{b} + \frac{1}{x}

{a \neq 0, b \neq 0, x \neq 0, x \neq - (a + b)}

Q. Solve for

x : \frac{1}{(a a + b + x)} = \frac{1}{a} + \frac{1}{b} + \frac{1}{x}, [a \neq 0, b \neq 0, x \neq 0, x \neq - (a + b)]

Q. Solve for x :
1/a+b+x = 1/a +1/b +1/x (a≠0, b≠0, x≠0).

Q. Solve for

x : \frac{1}{(a + b + x)} = \frac{1}{a} + \frac{1}{b} + \frac{1}{x}, [a \neq 0, b \neq 0, x \neq 0, x \neq - (a + b)]

Q. Solve

\frac{1}{a} - b + x = \frac{1}{x} + \frac{1}{a} - \frac{1}{b}

where

a \neq= 0

b \neq 0

x \neq 0

(

x = - a, x = b)

Join BYJU'S Learning Program

Solve for x 1a+b+x=1a+1b+1x,a+b≠0

1a+b+x−1x=1a+1bx−a−b−xx2+(a+b)x=a+bab−(a−b)x2+(a+b)x=a+bab−1x2+(a+b)x=1ab−ab=x2+(a+b)x⇒x2+(a+b)x+ab=0⇒x2+ax+bx+ab=0⇒x(x+a)+b(x+a)=0⇒(x+b)(x+a)=0⇒x=−b,−a

Solve for x
$\frac{1}{a + b + x} = \frac{1}{a} + \frac{1}{b} + \frac{1}{x}, a + b \neq 0$