Examples with solutions for Difference of squares: Using fractions

Exercise #1

(2x)23=6 (2x)^2-3=6

Video Solution

Step-by-Step Solution

First we rearrange the equation and set it to 0

4x236=0 4x^2-3-6=0

4x29=0 4x^2-9=0

We then apply the shortcut multiplication formula:

4(x294)=0 4(x^2-\frac{9}{4})=0

x2(32)2=0 x^2-(\frac{3}{2})^2=0

(x32)(x+32)=0 (x-\frac{3}{2})(x+\frac{3}{2})=0

x=±32 x=\pm\frac{3}{2}

Answer

±32 ±\frac{3}{2}

Exercise #2

(x+7)(x7)3=11x2 \frac{(x+7)(x-7)}{3}=-11-x^2

Video Solution

Answer

±2

Exercise #3

2x2328=x+42 \frac{2x^2-32}{8}=\frac{x+4}{2}

Video Solution

Answer

6

Exercise #4

Solve the following:


x(x29)x2+3x=0 \frac{x(x^2-9)}{x^2+3x}=0

Video Solution

Answer

3

Exercise #5

x264x8=17(x+8)64x2 \frac{x^2-64}{x-8}=\frac{17(x+8)}{64-x^2}

Video Solution

Answer

±47 ±\sqrt{47}