A complex fraction is a rational expression that has at least one fraction in its numerator or denominator, or both. We want to simplify the given complex fraction.
3x+ 4y/2x- 3y
To do so, we will combine the expressions in the numerator and those in the denominator. Then, we will multiply the new numerator by the reciprocal of the new denominator. Let's start by simplifying the numerator.
3/x+4/y
Note that neither denominator can be factored, and that there are no common factors between them. Therefore, the least common denominator (LCD) of this expressions is the product of the denominators.
xy
Now, we can add the expressions by rewriting each of them with the LCD.
Now, let's simplify the denominator.
2/x-3/y
To simplify the denominator, we can do it in the same way as the numerator. Notice that neither denominator can be factored, and that there are no common factors between them. Therefore, the LCD of these expressions is the product of the denominators.
xy
Now, we can subtract the expressions by rewriting each of them using the LCD.
Next, we can rewrite the complex fraction using the simplified components.
3x+ 4y/2x- 3y ⇔ 3y+4xxy/2y-3xxy
Finally, we will multiply the new numerator by the reciprocal of the new denominator.
3y+4xxy/2y-3xxy ⇔ 3y+4x/xy * xy/2y-3x
We can simplify this expression.
