# Solve the equation. 5((x+2)/(x-2))^2 - 2((x+2)/(x-2)) - 3 = 0 Hint: Use u = (x+2)/(x-2) and solve for x .  Enter the solutions separated by commas.

5((x+2)/(x-2))^2-2((x+2)/(x-2))-3=0

Substitution u=(x+2)/(x-2)

5u^2-2u-3=0

Now you use the formula for solution of quadratic equation

x_(1,2)=(-b pm sqrt(b^2-4ac))/(2a) where a,b and c are coefficients of the equation.

u_(1,2)=(2pmsqrt(4+60))/(-4)=(2pm8)/(-4)

u_1=-5/2, u_2=3/2

Now we put u_1 back in our substitution

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

Multiply whole equation by 4(x-2)

-5(x-2)=4(x+2)

-5x+10=4x+8

-9x=-2

x=2/9

Now we put u_2 back into our substitution. 

3/2=(x+2)/(x-2)

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5((x+2)/(x-2))^2-2((x+2)/(x-2))-3=0

Substitution u=(x+2)/(x-2)

5u^2-2u-3=0

Now you use the formula for solution of quadratic equation

x_(1,2)=(-b pm sqrt(b^2-4ac))/(2a) where a,b and c are coefficients of the equation.

u_(1,2)=(2pmsqrt(4+60))/(-4)=(2pm8)/(-4)

u_1=-5/2, u_2=3/2

Now we put u_1 back in our substitution

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

Multiply whole equation by 4(x-2)

-5(x-2)=4(x+2)

-5x+10=4x+8

-9x=-2

x=2/9

Now we put u_2 back into our substitution. 

3/2=(x+2)/(x-2)

Multiply whole equation by 2(x-2)

3(x-2)=2(x+2)

3x-6=2x+4

x=10

Hence your solutions are x_1=2/9  , x_2=10.

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