Verified answer

1/x = 1/b - 1/a

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

x = (ab)/(a - b)

Multiply to get rid of the fractions then solve for the variable:

1 / x + 1 / a = 1 / b

ab + bx = ax

ax - bx = ab

x(a - b) = ab

x = ab / (a - b)

Clearly the answer you have given is not correct, even if it was a typo.

(Ax + B) / (x^2 + a million) + (Cx + D) / (x^2 + 2) (Ax + B) * (x^2 + 2) + (Cx + D) * (x^2 + a million) = x^3 + x^2 + 2x + a million Ax^3 + Cx^3 + Bx^2 + Dx^2 + 2Ax + Cx + 2B + D = x^3 + x^2 + 2x + a million A + C = a million B + D = a million 2A + C = 2 2B + D = a million A + C = a million 2A + C = 2 2A + C - A - C = 2 - a million A = a million C = 0 2B + D - B - D = a million - a million B = 0 2B + D = a million D = a million (x + 0) * dx / (x^2 + a million) + (0x + a million) * dx / (x^2 + 2) x * dx / (x^2 + a million) + dx / (x^2 + 2) u = x^2 + a million du = 2x * dx x = sqrt(2) * tan(t) dx = sqrt(2) * sec(t)^2 * dt (a million/2) * du / u + sqrt(2) * sec(t)^2 * dt / (2 + 2 * tan(t)^2) => (a million/2) * du / u + (a million/sqrt(2)) * dt combine (a million/2) * ln|u| + (a million/sqrt(2)) * t + C => (a million/2)* ln|x^2 + a million| + (a million/sqrt(2)) * arctan(x / sqrt(2)) + C

1/x = 1/b - 1/a

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

x = ab / ( a - b )

1/x + 1/a = 1/b

or, 1/x = 1/b - 1/a

or, 1/x = (a - b)/(ab)

or, x = (ab)/(a - b)..........[as a ≠ b, a - b ≠ 0]

Multiply the entire equation by xba to get rid of all fractions.

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

So, we have ba + xb = xa

Place all terms concerning x onto one side to get

ba = xa -xb

Now factor out x on the right hand side.

ba = x(a - b)

Divide by (a - b) to isolate x.

x = ba / (a - b)

Hope this helps!

1/x = 1/b - 1/a

= (a-b)/ab

x = ab / (a-b)

your ans is right