Help With an Inequality Question Please

[val1]

Please can you help me with this question?

a) Sketch the curve \(\displaystyle \L y(x^2 - 2x - 3) = 9\)

[I'm not sure if this equation should read \(\displaystyle y = (x^2 - 2x - 3) = 9\), not that that makes any more sense to me]


b) Hence solve the inequality:

\(\displaystyle \L \frac{9}{{(x - 3)(x + 1)}} > 0\)

For part a) I factorised the quadratic expression in the bracket but was not sure what to do next. I'm ok about sketching a curve once I know where the points of interest are, but I'm not familiar with this type of expression. Do you think there is a typo, or am I missing something?

For part b), I'm not sure what to do with the '9' in the numerator or how to get started .

Please can you help? :?

 

[skeeter]

\(\displaystyle \frac{9}{(x-3)(x+1)} > 0\)

the left side of the inequality will never equal 0 because the numerator, 9, can never equal 0.

the inequality will be > 0 when the denominator is positive.

(x-3)(x+1) > 0 for values of x > 3 and x < -1, so the original inequality will be true for those values also.

part (a) is nonsense.

 

[pka]

I rather suspect that it is: graph
\(\displaystyle \L
y = \frac{9}{{x^2 - 2x - 3}}\).

That makes part b go with part a.

 

[val1]

Thanks for the reply guys. How would I sketch the curve in part b)?
Do you know what the points of intercept would be?

Thanks

 

[tkhunny]

You're kidding, right? Have you tried substituting x = 0 to find the y-intercept?

Substituting y=0 to find x-intercepts is a little harder, but only because there are none. Figure out how it is telling you that.