If P=
x
2
−16
x
2
−100
​
and Q=
x−4
x+10
​
, then the value of
Q
P
​
is:

First, let us simplify the expression for P using the algebraic identity a
2
−b
2
=(a−b)(a+b):

P=
x
2
−4
2

x
2
−10
2

​
=
(x−4)(x+4)
(x−10)(x+10)
​

We are given:

Q=
x−4
x+10
​

Now, calculate the ratio
Q
P
​
:

Q
P
​
=P×
Q
1
​

Q
P
​
=
(x−4)(x+4)
(x−10)(x+10)
​
×
x+10
x−4
​

Canceling out the common terms (x+10) and (x−4) from the numerator and denominator:

Q
P
​
=
x+4
x−10
​