What is ((x^2))/(((x-3)^2))>= 1 ?

The solution to ((x^2))/(((x-3)^2))>= 1 is 3/2 3

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((x^2))/(((x-3)^2))>= 1

\frac{( x ^{2} )}{( ( x - 3 ) ^{2} )} \geq 1

\frac{3}{2} \leq x < 3 or x > 3

Interval Notation

Decimal

1.5 \leq x < 3 or x > 3

Solution steps

\frac{x ^{2}}{( x - 3 ) ^{2}} \geq 1

Rewrite in standard form

\frac{6 x - 9}{( x - 3 ) ^{2}} \geq 0

Factor

\frac{6 x - 9}{( x - 3 ) ^{2}} : \frac{3 ( 2 x - 3 )}{( x - 3 ) ^{2}}

\frac{3 ( 2 x - 3 )}{( x - 3 ) ^{2}} \geq 0

Divide both sides by

3

\frac{\frac{3 ( 2 x - 3 )}{( x - 3 ) ^{2}}}{3} \geq \frac{0}{3}

Simplify

\frac{2 x - 3}{( x - 3 ) ^{2}} \geq 0

Identify the intervals

\frac{3}{2} \leq x < 3 or x > 3

\frac{( 3 x - 2 )}{( 2 x - 3 )} < 3

\frac{( x ^{2} - 5 ) ( x ^{2} - 4 )}{( x - 1 )} < 0

3 x^{2} - 8 x + 2 < 0

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

x^{5} - 7 x^{4} + 13 x^{3} - x^{2} - 14 x + 8 \leq 0

What is ((x^2))/(((x-3)^2))>= 1 ?
The solution to ((x^2))/(((x-3)^2))>= 1 is 3/2 <= x<3\lor x>3