Here is the problem:
5x/9x + 2/5 = 3x/4x + 6/7
(five ninths x plus two fifths equals three fourths x plus six sevenths)
Step one: Get the least common multiple (least common denominator) of the denominators.
To get the least common multiple of the denominators do the prime factorization of the denominators.
9 is prime
5 is prime
4
2 * 2 = 4
2 is prime
7 is prime
Multiply all the prime numbers together.
9*5*2*2*7
lcm(9,5,2,7) = 1260
Step two: Divide the least common multiple by the denominators
1260 / 9 = 140
1260 / 5 = 252
1260 / 2 = 630
1260 / 7 = 180
Step three: Multiply the above answer by the numerators
5x/9x + 2/5 = 3x/4x + 6/7
(five ninths x plus two fifths equals three fourths x plus six sevenths)
140 * 5 = 700
252 * 2 = 504
630 * 3 = 1890
180 * 6 = 1080
Which forms the equation:
700x + 504 = 1890x + 1080
Step four: Solve like a normal linear equation
Go to this post to see how: