Rearrange (r+s)/8s=(r-s)/8n to make r the subject
To rearrange the equation (r+s)/8s=(r-s)/8n to make r the subject, follow these steps:
Step 1: Expand the equation by cross-multiplying.
Multiply both sides of the equation by 8n:
8n * (r+s)/8s = 8n * (r-s)/8n
Step 2: Simplify the equation:
Cancel out the 8's:
n * (r+s)/s = (r-s)/n
Step 3: Remove the fraction by multiplying both sides by s:
s * n * (r+s)/s = s * (r-s)/n
Step 4: Simplify the equation:
Cancel out the 's' from the numerator and denominator on the left side:
n * (r+s) = s * (r-s)/n
Step 5: Expand the equation by cross-multiplying again:
Multiply both sides of the equation by n:
n * n * (r+s) = n * s * (r-s)/n
Step 6: Simplify the equation:
Cancel out the 'n' from the numerator and denominator on the right side:
n^2 * (r+s) = s * (r-s)
Step 7: Expand the equation:
Distribute n^2 on the left side:
n^2 * r + n^2 * s = s * r - s^2
Step 8: Rearrange the equation to have all the terms with 'r' on one side and other terms on the other side:
Move s * r term to the left side:
n^2 * r - s * r = - n^2 * s - s^2
Step 9: Factor out 'r' on the left side:
r * (n^2 - s) = - n^2 * s - s^2
Step 10: Divide both sides of the equation by (n^2 - s) to isolate 'r':
r = (- n^2 * s - s^2)/(n^2 - s)
Therefore, the equation rearranged to make 'r' the subject is:
r = (- n^2 * s - s^2)/(n^2 - s)
multiply both sides by 8sn, the LCD
n(r+s) = s(r-s)
expand
nr + ns = rs - s^2
get all terms containing r to one side
nr - rs = -ns - s^2
take out r as a common factor ...
I will let you finish it