Solve fractional inequalities that have quadratics \frac{2x^2+3x-2}{2x^2-3x-2}>0 How do you find the

wingtipti

wingtipti

Answered question

2022-01-29

Solve fractional inequalities that have quadratics
2x2+3x22x23x2>0
How do you find the range of solutions? Can you just bring the denominator onto the right hand side or does that lose solutions?

Answer & Explanation

ataill0k

ataill0k

Beginner2022-01-30Added 18 answers

Step 1
Another way of doing this kind of question is to multiply both sides by the denominator squared which, being non-negative, preserves the inequality.
So you could go straight to
(2x2+3x2)(2x23x2)>0
(2x1)(x+2)(2x+1)(x2)>0
You then just have to sketch a quick quartic graph showing the four roots and read off the solution sets.
Sean Becker

Sean Becker

Beginner2022-01-31Added 16 answers

Step 1
No, you cannot bring the denominator to the right. Thats

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