math help please :( rational

Question

The volume of a gas (V) increase or decrease with the temperature (T) according to charles law using the formula v1 over v2 = t1 over t2, Calculate V1 if v2= n²-144 over n-5, T1= n-5 over 3 and T2= n+12 over 6, then should be simplest form.

Answer 1

The expressions volume and temperature are

, and .

According to charles law

Sustitute the expression of v₁, T₁ and T₂ in the above.

Re-write the expression

is in the form

can be written as

Cancel the common terms

Therefore Volume of the gas at temperature T₁ is .