Question

solve the rational equation 1/(x+1)+2/(x+2)=3/(x+3)

Answer 1

help meee

Answer 2

Distribute, add like terms, solve for x.

Answer 3

$$\frac1{x+1}+\frac2{x+2}=\frac3{x+3}\\\frac{(x+2)(x+3)}{(x+1)(x+2)(x+3)}+\frac{2(x+1)(x+3)}{(x+1)(x+2)(x+3)}=\frac{3(x+1)(x+2)}{(x+1)(x+2)(x+3)}$$Getting everything to one side and combining the numerators now that we have a common denominator, we're left with$$\frac{(x+2)(x+3)+2(x+1)(x+3)-3(x+1)(x+2)}{(x+1)(x+2)(x+3)}=0$$It's clear that all that matters here is our numerator, since a rational expression only equals \(0\) when our numerator is \(0\). So we set the numerator to \(0\).$$(x+2)(x+3)+2(x+1)(x+3)-3(x+1)(x+2)=0$$Distribute and combine like terms:$$(x^2+5x+6)+2(x^2+4x+3)-3(x^2+3x+2)=0\\x^2+5x+6+2x^2+8x+6-3x^2-9x-6=0\\(1+2-3)x^2+(5+8-9)x+(6+6-6)=0\\0x^2+4x+6=0\\4x+6=0$$Can you solve from here?

Answer 4

no

Answer 5

\(4x+6=0\\4x=-6\\x=-\frac64=-\frac32\)