ANSWER
x = 5
EXPLANATION
[tex]\frac{-10}{x}=\frac{-16}{x+3}[/tex]
To solve this, we need x to be in the numerator of each fraction. To do that, we can multiply both sides by x:
[tex]\begin{gathered} \frac{-10}{x}\cdot x=\frac{-16}{x+3}\cdot x \\ -10=\frac{-16x}{x+3} \end{gathered}[/tex]
And also multiply both sides by (x+3):
[tex]\begin{gathered} -10(x+3)=\frac{-16x}{x+3}(x+3) \\ -10(x+3)=-16x \end{gathered}[/tex]
And now we have a very simple linear equation to solve.
First we have to distribute -10 into the sum inside the parenthesis:
[tex]-10x-30=-16x[/tex]
Now we add 16x on both sides of the equation:
[tex]\begin{gathered} -10x+16x-30=-16x+16x \\ 6x-30=0 \end{gathered}[/tex]
Add 30 on both sides:
[tex]\begin{gathered} 6x-30+30=30 \\ 6x=30 \end{gathered}[/tex]
And finally divide both sides by 6:
[tex]\begin{gathered} \frac{6x}{6}=\frac{30}{6} \\ x=5 \end{gathered}[/tex]
