Question

Solve the equation-

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Given info:- 5/(x-3) - 4/(x+4) = 1/x. And here the problem has asked to find out the value of x ?

Let's solve!!

Given equation is 5/(x-3) - 4/(x+4) = 1/x

⇛ [5(x+4) - 4(x-3)]/(x-3)(x+4) = 1/x

⇛ (5x+20-4x+12)/(x-3)(x+4) = 1/x

⇛ (x+32)/(x-3)(x+4) = 1/x

On applying cross multiplication then

⇛ x(x+32) = (x-3)(x+4)

⇛ x²+32x = x(x+4)-3(x+4)

⇛ x²+32x = x²+4x-3x-12

⇛ x²+32x = x²+x-12

⇛ x²+32x-x²-x = -12

⇛ (x²-x²)+(32x-x) = -12

⇛ 0+31x = -12

⇛ 31x = -12

⇛ x = -12/31

∴ x = -12/31

The value of x for the given problem -12/31

VERIFICATION:

Check

If x = -12/31 then LHS of the equation is

5/(x-3) - 4/(x+4)

⇛ 5/[(-12/31)-3] -4/[(-12/31)+4]

⇛ 5/[(-12-93)/31] -4/[(-12+124)/31]

⇛ 5/(-105/31) - 4/(112)/31

⇛ (5×-31)/105 - (4×31)/112

⇛ (-115/105)-(124/112)

⇛ (-31/21) - (31/28)

⇛ (-31)[(1/21)+(1/28)]

⇛ (-31)(21+28)/(21×28)

⇛ (-31×49)/(21×28)

⇛ (-31×7)/(21×4)

⇛-31/12

And RHS = 1/x

⇛ 1/(-12/31)

⇛ -31/12

⇛ LHS = RHS is true for x = -31/12