Question

Subtract: 2x+3 over x-4 minus x-5 over x+2

Answer 1

Start by getting a common denominator:
\[[(2x+3)/(x-4)]*[(x+2)/(x+2)]-[(x-5)/(x+2)]*[(x-4)/(x-4)]\].
This gives:
\[[(2x^2+4x+3x+6)-(x^2-4x-5x+20)]/[(x-4)(x-2)]\].
From here, distribute the negative and simplify:
\[Numerator:(2x^2-x^2+7x+9x+6-20)=x^2+16x-14\]
Final answer:
\[x^2+16x-14/(x-4)(x+2)\]

Answer 2

so the lcd is x-4?

Answer 3

the least common denominator is the multiplication of the two ((x+2)(x-4)) because you don't know what x is.

Answer 4

So in other words it would look like this:
\[\frac{x^2+16x-14}{(x-4)(x+2)}\]