Rational Equations

Question

begin with the fraction 4/9. now add a certain number x to the numerator and subtract x from the denominator and the result will be 3/10. find x.

Answer 1

start with 4/9; add x to the numerator and subtract x from the denominator; the result will be 3/10

 

so, our equation will be 4 + x / 9 - x = 3/ 10

 

step 1, cross multiply to get 10(4+x) = 3(9-x)

 

step 2, expand the parentheses to get 40 + 10x = 27 - 3x

 

step 3, combine like terms to get 13x = -13

 

so x = -1

 

Proof: 4+(-1)/9-(-1)= 3/10