Property 4
While doing simplification in equations, the expression is made equal to zero. The value of unknown variable is the element of the solution set. In rational expressions, the value that makes the denominator equal to zero is discarded from the solution set. This root is known as extraneous root of the equation.
Example
- \(\samefrac{(x-3)(x+5)}{x-3}=1\Rightarrow S.S.=\{-4\}\)
- \((x-3)(x+5)=(x-3)\Rightarrow S.S.=\{3,-4\}\)
1.
\(\left(x-2\right)\left(x-4\right)=\left(x-2\right)\)
\(\Rightarrow S.S.=?\)
2.
\(\left(x+1\right)\left(x-2\right)=\left(x+1\right)\)
\(\Rightarrow S.S.=?\)
3.
\(x^2-4=\left(x+2\right)\)
\(\Rightarrow S.S.=?\)
4.
\(\samefrac{\left(x-3\right)\left(x+1\right)}{\left(x-3\right)}=1\)
\(\Rightarrow S.S.=?\)
5.
\(\samefrac{x^2-4}{x-2}=1\)
\(\Rightarrow S.S.=?\)
6.
\(\left(x-3\right)\left(x-4\right)=\left(2x-6\right)\)
\(\Rightarrow S.S.=?\)
7.
\(x^2-9=\left(x-3\right)\)
\(\Rightarrow S.S.=?\)
8.
\(x^2-16=x-4\)
\(\Rightarrow S.S.=?\)
9.
\(\samefrac{\left(x-3\right)\left(x-2\right)}{\left(x-3\right)}=1\)
\(\Rightarrow S.S.=?\)
10.
\(\samefrac{\left(x+6\right)\left(x+4\right)}{\left(x+6\right)}=-2\)
\(\Rightarrow S.S.=?\)
11.
\(\left(x+1\right)\left(x+5\right)=\left(x+5\right)\)
\(\Rightarrow S.S.=?\)
12.
\(\left(x-2\right)\left(x-3\right)=\left(x-3\right)\)
\(\Rightarrow S.S.=?\)
13.
\(\samefrac{\left(x-5\right)\left(x+2\right)}{\left(x+2\right)}=1\)
\(\Rightarrow S.S.=?\)
14.
\(\samefrac{\left(x-4\right)\left(x+1\right)}{\left(x+1\right)}=1\)
\(\Rightarrow S.S.=?\)
15.
\(\left(x^2-9\right)=\left(3x+9\right)\)
\(\Rightarrow S.S.=?\)