Solving for a variable?

Question

Formula: 1/a + 1/b = 1/f Solve for a.

I know I have to subtract "1/b" to isolate "1/a" but after that, how do I get "a" by itself?

Answer 1

1/a + 1/b = 1/f

abf(1/a) + abf(1/b + abf(1/f)

bf + af = ab

Transpose af

bf + af - af = ab - af

bf = ab - af

bf = a(b - f)

Divide both sides of the equation by b - f

bf / b - f = a(b - f) / b - f

bf / b - f = a

- - - - - - - -s-

Answer 2

im not sure..but try it okay?

1/a+1/b=1/f

=> 1/a=1/f-1/b

=> a[1/a=1/f-1/b] (divide both sides by a)

=> 1=a/f-a/b

=>1=ab-af/fb (this is written as ab - af all over fb...fb is the LCD of a/f and a/b)

=>fb=ab-af (multiplying both sides by fb so that, the denominator would be cancelled)

=> fb= a (b-f) (a is a common factor in theright side)
=> fb/b-f=a (dividing both sides by b-f so that, a will remain on the right side)

the answer is:

a= fb/b-f

Answer 3

1/a+1/b=1/f
(transpose 1/b to the other side of the equation)
1/a = 1/f - 1/b
(simplify 1/f - 1/b)
1/a = b-f/fb
( get the reciprocal of the both sides to a)
a=fb/b-f

hope this help! and you understand my explanation

Answer 4

1/a + 1/b = 1/f
1/a = 1/f - 1/b
1/a = (b - f)/bf
a = bf/ (b - f)

Answer 5

1/a + 1/b = 1/f
Simplify:
1/a = 1/f - 1b
1/a = b/bf - f/bf
1a = (b - f)/bf
a = bf/(b - f)

Answer: bf/(b - f)