having trouble with solving more complicated Rational Inequalities

[AidanL06]

I'm confused on how to solve the question which states

[math]\frac{40x}{x^2+1} > \frac{45x}{x^2+8x+7}[/math]
I've had success trying to solve other inequalities that are more simple but this one just isn't working in my brain

Please help

 

[stapel]

I'm confused on how to solve the question which states

[math]\frac{40x}{x^2+1} > \frac{45x}{x^2+8x+7}[/math]

Follow the usual procedure: Get all terms on one side of the inequality symbol, and combine the fractions into one. Factor and find the zeroes of the numerator and denominator. Use these zeroes to split the number line into intervals. Then test on each interval.

 

[Dr.Peterson]

I'm confused on how to solve the question which states

[math]\frac{40x}{x^2+1} > \frac{45x}{x^2+8x+7}[/math]
I've had success trying to solve other inequalities that are more simple but this one just isn't working in my brain

Please help

Please show us the trouble you're having, so we can see where you need help.

 

[Dr.Peterson]

I'm confused on how to solve the question which states

[math]\frac{40x}{x^2+1} > \frac{45x}{x^2+8x+7}[/math]
I've had success trying to solve other inequalities that are more simple but this one just isn't working in my brain

This is different from most (so much so that you should check whether you copied it correctly), but can be solved.

You'll have two quadratic factors that can't be factored the usual way; one can't be factored over the reals, and is always positive; the other can be factored over the reals (using the quadratic formula to find the zeros). You'll end up with 5 points dividing the number line into 6 parts to check.