Question

For what value of n is n+1P3=nP4

Answer 1

n= P3 / (p2+1) (p+1) (p-1)

Answer 2

Answer:

$n=\frac{-p^{3} }{(1+p^{2})(1+p)(1-p) }$

Step-by-step explanation:

To find the value of n we must solve the equation for n.

The equation can be written as:

$n + p^{3} = np^{4}$

We are going to move the terms with n to the left and the terms without n to the right:

$n + p^{3} = np^{4}\\n-np^{4} =-p^{3}$

Now we will proceed to factor the left side of the equation and solve for n:

$n-np^{4} =-p^{3}\\n(1-p^{4})=-p^{3}  \\n(1+p^{2})(1-p^{2} )=-p^{3} \\n(1+p^{2} )(1+p)(1-p)=-p^{3} \\n=\frac{-p^{3} }{(1+p^{2})(1+p)(1-p) }$

Therefore $n=\frac{-p^{3} }{(1+p^{2})(1+p)(1-p) }$