# What value of k makes the following equation true?

(2a + 4 / 2a - 1) - (k / a + 5) = 21a + 17 / (2a - 1)(a + 5)

### 1 Answer

- 8 years agoFavorite Answer
If "k" is meant to have just a numerical value, then you can simply plug in any number for "a" and easily solve this. If "k" represents more than just a variable but an expression, try setting all individual parts with the same denominator, (2a-1)(a+5). You can do this by multiplying each expression by (2a-1)(a+5) / (2a-1)(a+5).

For example, the left side of the equation becomes:

(2a+4)(a+5) / (2a-1)(a+5) - k(2a-1) / (2a-1)(a+5) ---> (2a+4)(a+5)-k(2a-1) / (2a-1)(a+5)

and the right:

21a(2a-1)(a+5) / (2a-1)(a+5) + 17/(2a - 1)(a + 5) ---> 21a(2a-1)(a+5)+17 / (2a - 1)(a + 5)

multiplying out:

(2a^2+14a+20-2ka+k) / (2a-1)(a+5) = 42a^3+189a^2-105a / (2a-1)(a+5)

you can now ignore the denominator since we have set them equal:

2a^2+14a+20-2ka+k = 42a^3+189a^2-105a

solve for k:

k = (42a^3 + 187a^2 -119a - 20) / (-2a+1)

No idea if this is remotely right as I just threw it together as I havent tested it and there could be mistakes

edit: tried it w/ a=0, doesnt come out right, but I am sure the method would work if you actually wrote it down and went step by step