Put into standard form
3/x + 4/y = 2
To put the equation 3/x + 4/y = 2 into standard form, we need to eliminate the fractions by finding a common denominator.
First, let's find the least common multiple (LCM) of x and y, which will be the common denominator. To find the LCM, we factorize x and y as much as possible.
For x: x has only one term, so it cannot be factorized any further.
For y: y has only one term, so it cannot be factorized any further.
The LCM of x and y is simply the product xy. Therefore, the common denominator for our fractions is xy.
Now, we'll multiply every term in the equation by xy to eliminate the fractions:
xy * (3/x) + xy * (4/y) = xy * 2
Now, simplify each term:
3y + 4x = 2xy
Finally, rearrange the terms so that the equation is in standard form:
2xy - 4x - 3y = 0
So, the given equation 3/x + 4/y = 2 in standard form is 2xy - 4x - 3y = 0.