What is (x^2+(4x^2))/(((x-2)^2))<= 5 ?

The solution to (x^2+(4x^2))/(((x-2)^2))<= 5 is x<= 1

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(x^2+(4x^2))/(((x-2)^2))<= 5

\frac{x ^{2} + ( 4 x ^{2} )}{( ( x - 2 ) ^{2} )} \leq 5

x \leq 1

Interval Notation

(- \infty, 1]

Solution steps

\frac{x ^{2} + 4 x ^{2}}{( x - 2 ) ^{2}} \leq 5

Rewrite in standard form

\frac{20 x - 20}{( x - 2 ) ^{2}} \leq 0

Factor

\frac{20 x - 20}{( x - 2 ) ^{2}} : \frac{20 ( x - 1 )}{( x - 2 ) ^{2}}

\frac{20 ( x - 1 )}{( x - 2 ) ^{2}} \leq 0

Divide both sides by

20

\frac{\frac{20 ( x - 1 )}{( x - 2 ) ^{2}}}{20} \leq \frac{0}{20}

Simplify

\frac{x - 1}{( x - 2 ) ^{2}} \leq 0

Identify the intervals

x \leq 1

(3 x + 1)^{2} + 4 x < 9 x^{2} + x - 4

((x^{2} - 5 x + 6)^{2})^{0} ((x^{2} - 11 x + 24)^{3})^{1} > 0

\frac{( 2 ( x - 4 ) )}{( ( x - 1 ) ( x - 7 ) )} \geq \frac{1}{( x - 2 )}

- 3 m^{2} + 2 m + 1 \leq 0

\frac{- 1}{( x + 3 )} > 0

What is (x^2+(4x^2))/(((x-2)^2))<= 5 ?
The solution to (x^2+(4x^2))/(((x-2)^2))<= 5 is x<= 1