What is ((x-6)^5(x-5)^6)/((x-1))<0 ?

The solution to ((x-6)^5(x-5)^6)/((x-1))<0 is 1<x<5\lor 5<x<6

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((x-6)^5(x-5)^6)/((x-1))<0

\frac{( x - 6 ) ^{5} ( x - 5 ) ^{6}}{( x - 1 )} < 0

1 < x < 5 or 5 < x < 6

Interval Notation

(1, 5) \cup (5, 6)

Solution steps

\frac{( x - 6 ) ^{5} ( x - 5 ) ^{6}}{x - 1} < 0

Rewrite in standard form

\frac{( 120 x ^{5} + 5 ( - 720 x ^{4} + 155520 x ) + 10 ( 4320 x ^{3} - 25920 x ^{2} ) - 933120 ) ( 720 x ^{6} - 1800000 x ^{3} + 6 ( - 3600 x ^{5} - 2250000 x ) + 15 ( 18000 x ^{4} + 450000 x ^{2} ) + 11250000 )}{x - 1} < 0

Factor

\frac{( 120 x ^{5} + 5 ( - 720 x ^{4} + 155520 x ) + 10 ( 4320 x ^{3} - 25920 x ^{2} ) - 933120 ) ( 720 x ^{6} - 1800000 x ^{3} + 6 ( - 3600 x ^{5} - 2250000 x ) + 15 ( 18000 x ^{4} + 450000 x ^{2} ) + 11250000 )}{x - 1} : \frac{86400 ( x - 6 ) ^{5} ( x - 5 ) ^{6}}{x - 1}

\frac{86400 ( x - 6 ) ^{5} ( x - 5 ) ^{6}}{x - 1} < 0

Divide both sides by

86400

\frac{\frac{86400 ( x - 6 ) ^{5} ( x - 5 ) ^{6}}{x - 1}}{86400} < \frac{0}{86400}

Simplify

\frac{( x - 6 ) ^{5} ( x - 5 ) ^{6}}{x - 1} < 0

Identify the intervals

1 < x < 5 or 5 < x < 6

(81)^{\frac{1}{4}}

16 x^{2} - 48 x y + 36 y^{2}

k^{2} - 6 = 43

∣ 18 x ∣ = 0

\frac{n}{3} \geq - 6

What is ((x-6)^5(x-5)^6)/((x-1))<0 ?
The solution to ((x-6)^5(x-5)^6)/((x-1))<0 is 1<x<5\lor 5<x<6