Make x the subject of the relation:1+ax 1 -ax =p/q
If you mean
(1+ax)/(1-ax) = p/q
q(1+ax) = p(1-ax)
q + aqx = p - apx
aqx+apx = p-q
x(ap+aq) = p-q
x = (p-q) / a(p+q)
To make x the subject of the relation given by "1 + ax / (1 - ax) = p/q," we will isolate x on one side of the equation.
Let's break down the steps:
1. Start by multiplying both sides of the equation by (1 - ax) to eliminate the fraction:
(1 - ax) * (1 + ax) / (1 - ax) = (p/q) * (1 - ax)
Simplifying the left side of the equation:
1 + ax = (p/q) * (1 - ax)
2. Distribute (p/q) to both terms on the right side:
1 + ax = (p/q) - (p/q) * ax
3. Move the ax term to the left side of the equation by subtracting ax from both sides:
1 + ax - ax = (p/q) - (p/q) * ax- ax
1 = (p/q) - (p/q) * ax - ax
4. Combine like terms on the right side:
1 = (p/q) - ax * (1 + p/q)
5. Move the ax term to the left side by adding ax to both sides:
1 + ax = (p/q) - ax * (1 + p/q) + ax
6. Simplify the right side:
1 + ax = (p/q) - (ax + ax * p/q)
7. Group the ax terms on the right side:
1 + ax = (p/q) - ax * (1 + p/q)
8. Move the (1 + ax) term to the right side by subtracting it from both sides:
1 = (p/q) - ax * (1 + p/q) - ax
9. Combine like terms on the right side:
1 = (p/q) - ax - ax * (1 + p/q)
10. Move the ax terms to the left side by adding ax and ax * (1 + p/q) to both sides:
1 + ax + ax * (1 + p/q) = (p/q)
11. Distribute ax to (1 + p/q):
1 + ax + ax + (ax * p/q) = (p/q)
12. Simplify further:
1 + 2ax + (ax * p/q) = (p/q)
13. Subtract 1 from both sides:
2ax + (ax * p/q) = (p/q) - 1
14. Factor out ax:
ax * (2 + p/q) = (p/q) - 1
15. Finally, divide both sides by (2 + p/q) to solve for x:
ax = (p/q - 1) / (2 + p/q)
16. Divide both sides by a to isolate x:
x = ((p/q - 1) / (2 + p/q)) / a
Thus, x is the subject of the relation given by x = ((p/q - 1) / (2 + p/q)) / a.