What is (x-1)/(x-4)<(x-3)/(x-2) ?

The solution to (x-1)/(x-4)<(x-3)/(x-2) is x<2\lor 5/2 <x<4

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(x-1)/(x-4)<(x-3)/(x-2)

\frac{x - 1}{x - 4} < \frac{x - 3}{x - 2}

x < 2 or \frac{5}{2} < x < 4

Interval Notation

(- \infty, 2) \cup (\frac{5}{2}, 4)

Decimal Notation

x < 2 or 2.5 < x < 4

Solution steps

\frac{x - 1}{x - 4} < \frac{x - 3}{x - 2}

Rewrite in standard form

\frac{4 x - 10}{( x - 4 ) ( x - 2 )} < 0

Factor

\frac{4 x - 10}{( x - 4 ) ( x - 2 )} : \frac{2 ( 2 x - 5 )}{( x - 4 ) ( x - 2 )}

\frac{2 ( 2 x - 5 )}{( x - 4 ) ( x - 2 )} < 0

Divide both sides by

2

\frac{\frac{2 ( 2 x - 5 )}{( x - 4 ) ( x - 2 )}}{2} < \frac{0}{2}

Simplify

\frac{2 x - 5}{( x - 4 ) ( x - 2 )} < 0

Identify the intervals

x < 2 or \frac{5}{2} < x < 4

20 = v - 13

2 - \frac{5}{3}

\frac{( a ^{3} + 1 )}{( a ^{4} - a ^{3} + a - 1 )}

4^{12}

x^{2} - 10 x - 11 = 0

What is (x-1)/(x-4)<(x-3)/(x-2) ?
The solution to (x-1)/(x-4)<(x-3)/(x-2) is x<2\lor 5/2 <x<4