Square of Difference: Equations with denominators

Using quadrilateralsComplete the missing numbersData with powers and rootsMore than one factorizationNumber of termsIdentify the greater valueUsing fractionsEquations with variables on both sidesResulting in a quadratic equationSystem of equations with no solutionUsing multiple rulesSolving the problemTransition between expressions
Question 1

Solve the following equation:

\( \frac{1}{(x-2)^2}+\frac{1}{x-2}=1 \)

Question 2

Solve the following equation:

\( \frac{x^3+1}{(x-1)^2}=x+4 \)

Question 3

Solve the following equation:

\( \frac{(2x-1)^2}{x-2}+\frac{(x-2)^2}{2x-1}=4.5x \)

Examples with solutions for Square of Difference: Equations with denominators

Exercise #1

Solve the following equation:

1(x−2)2+1x−2=1 \frac{1}{(x-2)^2}+\frac{1}{x-2}=1

Video Solution

Answer

12[5±5] \frac{1}{2}[5\pm\sqrt{5}]

Exercise #2

Solve the following equation:

x3+1(x−1)2=x+4 \frac{x^3+1}{(x-1)^2}=x+4

Video Solution

Answer

x=3,12 x=3,\frac{1}{2}

Exercise #3

Solve the following equation:

(2x−1)2x−2+(x−2)22x−1=4.5x \frac{(2x-1)^2}{x-2}+\frac{(x-2)^2}{2x-1}=4.5x

Video Solution

Answer

−1±3 -1\pm\sqrt{3}