Square of sum: Equations with denominators

Equations with Variables on One SideUsing short multiplication formulasUsing variablesComplete the missing numbersIdentify the greater valueUsing fractionsUsing quadrilateralsMore than one factorizationSystem of equations with no solutionData with powers and rootsUsing multiple rulesNumber of termsEquations with variables on both sidesSolving the problemTransition between expressionsResulting in a quadratic equation
Question 1

Solve the following equation:

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

Question 2

Solve the following equation:

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

Question 3

Look at the following equation:

\( \frac{\sqrt{x}-\sqrt{x+1}}{x+1}=1 \)

This can also be written as:

\( x[A(x+B)-x^3]=0 \)

Calculate A and B.

Question 4

Look at the following equation:

\( \frac{\sqrt{x}+\sqrt{x+1}}{x+1}=1 \)

The same equation can be presented as follows:

\( x[A(x+B)-x^3]=0 \)

Calculate A and B.

Examples with solutions for Square of sum: Equations with denominators

Exercise #1

Solve the following equation:

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

Video Solution

Answer

−12[1±5] -\frac{1}{2}[1\pm\sqrt{5}\rbrack

Exercise #2

Solve the following equation:

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

Video Solution

Answer

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

Exercise #3

Look at the following equation:

x−x+1x+1=1 \frac{\sqrt{x}-\sqrt{x+1}}{x+1}=1

This can also be written as:

x[A(x+B)−x3]=0 x[A(x+B)-x^3]=0

Calculate A and B.

Video Solution

Answer

B=1 , A=4

Exercise #4

Look at the following equation:

x+x+1x+1=1 \frac{\sqrt{x}+\sqrt{x+1}}{x+1}=1

The same equation can be presented as follows:

x[A(x+B)−x3]=0 x[A(x+B)-x^3]=0

Calculate A and B.

Video Solution

Answer

B=1 , A=4