Question

how can we get [4/x-3]-[1/x+2] from [3x+11]/[x^2-x-6] step by step

Answer 1

Method for combining rational functions (aka fraction functions):
Step 1: find a common denominator. if you don't know, multiply all the denominators together, that will be your common denominator. as for the numerators, multiply them by your common denominator excluding whatever was your original denominator: \[(x-3)(x+2)=(x^2-x-6)\] numerator 1:\[4/(x-3) * (x+2)/(x+2)=4(x+2)/(x^2-x-6)=(4x+8)/(x^2-x-6)\] numerator 2:\[1/(x+2)*(x-3)/(x-3)=(x-3)/(x^2-x-6)\]

Step 2: add/subtract
\[((4x+8-(x-3))/(x^2-x-6)=(3x+11)/(x^2-x-6)\]

Answer 2

thank you very much

Answer 3

no problem (: