[tex]x\text{ = -4 or -8}[/tex]
Here, we want to aolve for the value of x
We proceed by cross-multiplying
We have this as follows;
[tex]\begin{gathered} \frac{1}{x+3}\text{ = }\frac{x+10}{x-2} \\ \\ 1(x-2)\text{ = (x+3)(x+10)} \\ x-2\text{ = x(x+10) + 3(x+10)} \\ x-2=x^2+10x+3x+30 \\ x-2=x^2+13x+30 \\ x^2+13x-x+30+2\text{ = 0} \\ x^2+12x+32\text{ = 0} \\ x^2+4x+8x+32\text{ = 0} \\ x(x+4)\text{ + 8(x+4)= 0} \\ (x+4)(x+8)\text{ = 0} \\ x\text{ + 4 = 0 or x + 8 = 0} \\ x\text{ = -4 or -8} \end{gathered}[/tex]
