Porisma

Worked solution

Rearrange an exponential fraction

Given that 10+v10−v=Aet\dfrac{10+v}{10-v}=Ae^t, express vv in terms of AA and tt.

[N2011/I/8(modified)]

CJC · Discussion · Question 1

Answer

v=(10Aet−10)/(Aet+1)v=(10Ae^t-10)/(Ae^t+1), provided Aet≠−1Ae^t\ne-1.

Clear the original denominator

The original expression requires v≠10v\ne10. Multiplying gives 10+v=Aet(10−v)10+v=Ae^t(10-v).

How did this part go?

Collect and factor v

Aetv+v=10Aet−10Ae^tv+v=10Ae^t-10, so v(Aet+1)=10Aet−10v(Ae^t+1)=10Ae^t-10. Therefore

v=10Aet−10Aet+1.v=\frac{10Ae^t-10}{Ae^t+1}.

This requires Aet≠−1Ae^t\ne-1; if Aet=−1Ae^t=-1, the original equation would give 10=−1010=-10 and has no solution.

How did this part go?

Common mistakes

Check denominators before multiplying and before dividing.

Solution notes

The page header says JC2 but the tutorial title says 2025/JC1; both remain in the native record.

Read the hint