Step-by-step explanation:
Here are the general steps for adding and subtracting rational expressions:
Find the LCD (least common denominator) of the expressions. To do this, factor the denominators and then multiply the factors together, taking the highest power of each factor. This will give you the LCD.
Rewrite each expression so that the denominator is the LCD. To do this, multiply both the numerator and the denominator by the appropriate factor(s) so that the denominator matches the LCD.
Combine the numerators of the expressions by adding or subtracting them, depending on whether you are adding or subtracting the expressions.
Simplify the resulting expression by factoring, if possible, and then canceling out common factors in the numerator and denominator.
Here is an example of how to add and subtract rational expressions:
Find the LCD of the expressions:
3 4
--- + ---
2x x-3
The factors of the denominators are 2, x, and x-3. The highest power of 2 is 2, the highest power of x is x, and the highest power of x-3 is x-3. So the LCD is 2x(x-3).
Rewrite each expression with the LCD:
3(x-3) 4(2x)
--------- + ---------
2x(x-3) (x-3)(2x)
Combine the numerators:
3(x-3) + 4(2x)
2x(x-3)
3x - 9 + 8x
2x(x-3)
Simplify the resulting expression:
11x - 9
2x(x-3)
This is the final answer.
When subtracting rational expressions, you simply change the sign of the second expression and then follow the same steps as above for adding.