Question

solve for x : 1/a+b+x-1/x=1/a+1/b​

Answer 1

Answer:

1/b and -b/2

Step-by-step explanation:

1/a+b+x-1/x=1/a+1/b

b+x-1/x=1/b

x^2b-(1-b^2)x-b=0

using quadratic equation formula

we get x=1/b,-b/2

Answer 2

Answer:

x = -2b or -2a

Step-by-step explanation:

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

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

x-(a+b+x)/x(a+b+x) = a+b/ ab

-1(a+b) /x(a+b+x) = a+b/ ab

-1(a+b)/(a+b) = x(a+b+x)/ab

-1=x(a+b+x) / ab

-ab= (a+b)x + x2

so, x2 + (a+b)x +ab = 0

now, A = 1, B=(a+b) C= ab..

so, D = B2 - 4AC

 =(a+b)2 - 4ab

 = (a-b)2

so, x = (-B + √D)/2A  and (-B-√D)/2A

 = -a-b+a-b /2*1   and  -a-b-a+b /2*1

 = -2b/1  and -2a /1

so,x = -2b or -2a

HOPE THIS HELPS YOU...........

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