Question

Simplify into one fraction -2/x+3 - 4/x-5

Answer 1

You have to multiply each term by what it's missing for the denominators to both be the same. The first term has x+3 but is missing x-5 so multiply top and bottom by x-5 and then distribute the numerator to -2x + 10. Do the same for the other term that is missing the x+3 and distribute to get -(4x+12). Distribute the negative in then simplify to get
`(-6x-2)/((x+3)(x-5))` or simplify even further to get
`(-2(3x+1))/((x+3)(x-5))`

Answer 2

Multiply and divide by the product of the denominators.

`(-2)/(x+3)+(-4)/(x-5)=(-2(x-5)-4(x+3))/((x+3)(x-5))\\\\=(-6x-2)/(x^(2)-2x-15)`