Question

Find the solutions of∅¬¬: 1/(x+a) - 1/(x+b) = 1/a x 1/b

Answer 1

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

First, rewrite this as 1/(x+a) - 1/(x+b) = (1/a)(1/b) (do not use "x" to indicate mult.)

Then the LCD is (x+a)(x+b)(ab)

so the first term becomes (x+b)(ab), and
the second becomes (x+a)(ab), and
the third becomes (x+a)(x+b).

Thus, we now have (x+b)(ab) - (x+a)(ab) = (x+a)(x+b)(b) + (x+a)(x+b)(a).

Now, with the fractions gone, can you solve thios for x?