Question

Five rational function equations to help me with, if you'd be oh so kind.

(5x+1)/x < 1

Answer 1

Ok i have an idea but i might be wrong so hopefully this might help.
https://www.khanacademy.org/math/algebra2/rational-expressions/solving-rational-equations/v/solving-rational-equations-2

Answer 2

Im sorry ; ~;

Answer 3

\[\frac{5x+1}{x}<1\\
\frac{5x}x+\frac1x<1\\
\quad\dots\quad<1\]

Answer 4

the first term simplifies . . .

Answer 5

5x^2 + 1/x <1?

Answer 6

not quite, the x's in the first term dont multiply, they cancel

Answer 7

Oh. Okay so 5 + 1/x <1?

Answer 8

good, now the next step is to take away 5 form both sides

Answer 9

*from

Answer 10

1/x < -4

Answer 11

yes

Answer 12

now if we multiply both sides by x . . .

Answer 13

1 = -4x

So x = -1/4

Answer 14

we get

-1/4 < x


but this is because we assumed that x was not negative
(we didn't swap the direction of inequality)

Answer 15

if we had assumed that x was negative, we would have switched the direction of inequality, when we multiplied both sides by x,


we would have gotten
-1/4 > x

Answer 16

hmmm,

Answer 17

Okay thanks. For this next one (assuming we're good here), wouldn't I just want to find the quadratic parts?