An equation is formed of two equal expressions. The least common denominator is 3x(x+1) and the equation will have 2 valid solutions.
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
A.) The least common denominator of the equation,
[tex]\dfrac{1}{x} + \dfrac{2}{x+10} - \dfrac13=0\\\\\\\dfrac{1 \times (x+10) \times 3}{x\times (x+10) \times 3} + \dfrac{2\times 3 \times x}{(x+10)\times 3 \times x} - \dfrac{1 \times x \times (x+10)}{3 \times x \times (x+10)}=0\\\\\\\dfrac{-x^2-x+30}{3x(x+10)} = 0[/tex]
B.) The valid solutions to the equations are:
[tex]\dfrac{1}{x} + \dfrac{2}{x+10} = \dfrac13\\\\\dfrac{1(x+10)+2(x)}{x(x+10)} = \dfrac13\\\\\dfrac{x+10+2x}{x^2+10x} = \dfrac13\\\\\\[/tex]
3x + 30 + 6x= x^2 + 10x
9x + 30 = x^2 + 10x
x^2+x-30=0
x^2+6x-5x-30=0
x(x+6)-5(x+6)=0
(x-5)(x+6)=0
x= 5,6
Hence, The least common denominator is 3x(x+1) and the equation will have 2 valid solutions.
Learn more about Equation:
https://brainly.com/question/2263981
#SPJ2
