3/p-1=4/2p+1

Solution for 3/p-1=4/2p+1 equation:

3/p-1=4/2p+1

We move all terms to the left:

3/p-1-(4/2p+1)=0


Domain of the equation: p!=0

p∈R



Domain of the equation: 2p+1)!=0

p∈R


We get rid of parentheses

3/p-4/2p-1-1=0

We calculate fractions


6p/2p^2+(-4p)/2p^2-1-1=0

We add all the numbers together, and all the variables

6p/2p^2+(-4p)/2p^2-2=0

We multiply all the terms by the denominator


6p+(-4p)-2*2p^2=0

Wy multiply elements

-4p^2+6p+(-4p)=0

We get rid of parentheses

-4p^2+6p-4p=0

We add all the numbers together, and all the variables

-4p^2+2p=0

a = -4; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-4)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-4}=\frac{-4}{-8}
=1/2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-4}=\frac{0}{-8}
=0
$