Calculus, solve inequation 2x-3 > -4X/x-1 ? thx la lot?

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A few days ago

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2x – 3 > -4x / (x-1)

simplify this to:

(x-1)(2x-3) > -4x

and open up equation to

2x^2 -3x – 2x + 3 > -4x

2x^2 -5x + 3 + 4x > 0

2x^2 -x + 3 > 0

now multiple each side by -1 to give

-2x^2 + x – 3 > 0

and simplify this to

(-2x + 3) (x + 1) > 0

from this, we know that when

x < -3/2 or x > -1/ the equation cannot be true (just try substituting numbers outside these ranges)

and so:

-3/2 < x < -1 i.e. x must be between -3/2 and -1 to hold true

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