solve for g. R=(g*s)/(g+s)
invert and separate terms ... 1 / R = [g / (g*s)] + [s / (g*s)]
1 / R = (1 / s) + (1 / g) ... 1 / g = (1 / R) - (1 / s) = [s / (R*s)] - [R / (R*s)]
1 / g = (s - R) / (R*s) ... g = (R*s) / (s - R)
R=(g*s)/(g+s)
R(g+s) = gs
Rg+Rs = gs
g(s-R) = Rs
g = Rs/(s-R)
To solve for g in the equation R=(g*s)/(g+s), we can follow these steps:
Step 1: Multiply both sides of the equation by g + s to remove the denominator.
R(g + s) = g * s
Step 2: Distribute R to both terms inside the parentheses.
R * g + R * s = g * s
Step 3: Move all the terms with g on one side of the equation and all the other terms on the other side.
R * g - g * s = - R * s
Step 4: Factor out the common factor g.
g * (R - s) = - R * s
Step 5: Divide both sides of the equation by (R - s).
g = (- R * s) / (R - s)
Therefore, the solution for g in terms of R and s is g = (- R * s) / (R - s).
If you have specific values for R and s, you can substitute them into the equation to find the numerical value of g.