Question

How do you solve the rational equation `4/(x+2)-3/(x-5)=15/(x^2-3x-10)`?

Answer 1

x = 41

Explanation:

Firstly: factor the denominator on the right side.

`x^2 - 3x - 10 = (x - 5 )( x + 2 )`

Equation now becomes :

`4/(x+2) - 3/(x-5 ) = 15/((x-5)(x+2))`

Multiply each term on both sides by (x-5)(x+2)

`( 4(x-5)cancel(x+2))/cancel(x+2) - (3cancel(x-5)(x+2))/cancel(x-5)`= `(15cancel(x-5)cancel(x+2))/(cancel(x-5)cancel(x+2))`

which simplified becomes : 4(x-5) -3(x+2) = 15

hence 4x - 20 - 3x - 6 = 15

therefore x = 15+6+20 = 41