Q. Add.The numerator should be expanded and simplified. The denominator should be either expanded or factored.x−32+x+15=
Find common denominator: To add the two fractions, we need a common denominator. The common denominator for (x−3) and (x+1) is the product of the two, which is (x−3)(x+1).
Rewrite fractions with common denominator: We will rewrite each fraction with the common denominator. For the first fraction, we multiply the numerator and denominator by (x+1), and for the second fraction, we multiply the numerator and denominator by (x−3).
Expand the numerators: After rewriting, we have: (x−3)(x+1)2⋅(x+1)+(x−3)(x+1)5⋅(x−3)
Combine numerators over common denominator: Now we expand the numerators:(2x+2)/((x−3)(x+1))+(5x−15)/((x−3)(x+1))
Simplify the numerator: Next, we combine the numerators over the common denominator: egin{equation}\frac{2x + 2 + 5x - 15}{(x−3)(x+1)}\end{equation}
No further simplification possible: We simplify the numerator by combining like terms: egin{equation}\frac{7x - 13}{(x−3)(x+1)}\end{equation}
No further simplification possible: We simplify the numerator by combining like terms: (7x−13)/((x−3)(x+1))The expression is now simplified, and there is no further simplification possible for the denominator since it is already factored and does not have common factors with the numerator.
More problems from Factor sums and differences of cubes