# Dividing vs. subtracting to get all terms with one variable to one side of equation

#### find_the_fun

##### Active member
If you have the equation $$\displaystyle \frac{dx}{dt}=4(x^2+1)$$ I sometimes get confused if i should should subtract $$\displaystyle 4(x^2+1)$$ from both sides or multiply by it's reciprocal. If I subtract from both sides then I'd have 0 on the right side and that would give a different answer after integration but mathematically why would it be wrong?

#### chisigma

##### Well-known member
Re: Dividing vs subtracting to get all terms with one variable to one side of equation

If you have the equation $$\displaystyle \frac{dx}{dt}=4(x^2+1)$$ I sometimes get confused if i should should subtract $$\displaystyle 4(x^2+1)$$ from both sides or multiply by it's reciprocal. If I subtract from both sides then I'd have 0 on the right side and that would give a different answer after integration but mathematically why would it be wrong?
Since for all real x is $4\ (x^{2} + 1) > 0$ You can devide both sides by $4\ (x^{2} + 1)$ without danger and then integrate separately in x and y...

Kind regards

$\chi$ $\sigma$

#### MarkFL

If you have the equation $$\displaystyle \frac{dx}{dt}=4(x^2+1)$$ I sometimes get confused if i should should subtract $$\displaystyle 4(x^2+1)$$ from both sides or multiply by it's reciprocal. If I subtract from both sides then I'd have 0 on the right side and that would give a different answer after integration but mathematically why would it be wrong?