Question

1. For what values of x does the function y=2x+13 take on a positive value? a negative value?

2.
 a+3 over (a^2−1) − 1 over (a^2+a)

Answer 1

`2x+13=0\\ 2x=-13\\ x=-6.5`

The function is linear where
`a\ \textgreater \ 0`, so it's negative for
`x\ \textless \ -6.5` and positive for
`x\ \textgreater \ -6.5`

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`D:x\in\mathbb{R}\setminus\{-1,1,0\}\\\\ (a+3)/(a^2-1) - (1)/(a^2+a)=\\ (a+3)/((a-1)(a+1)) - (1)/(a(a+1))=\\ (a(a+3))/(a(a-1)(a+1)) - (a-1)/(a(a-1)(a+1))=\\ (a^2+3a-a+1)/(a(a-1)(a+1))=\\ (a^2+2a+1)/(a(a-1)(a+1))=\\ ((a+1)^2)/(a(a-1)(a+1))=\\ (a+1)/(a(a-1))`

for
`a\in(-\infty,-1)` it's negative
for
`a\in(-1,0)` it's positive
for
`a\in(0,1)` it's negative
for
`a\in(1,\infty)` it's positive