y = (1+x)/(1-x)
How do I rearrange that equation to be:
x = (y-1)/(y+1)
multiply both sides by 1-x
y-xy=1+x
subtract one, add xy to each side
y-1=x+xy=x(1+y)
solve for x.
Ah, thanks so much. My mind is working slowly today :)
To rearrange the equation y = (1+x)/(1-x) to the form x = (y-1)/(y+1), we will follow these steps:
Step 1: Expanding the numerator
Multiply both sides of the equation by (1-x) to eliminate the denominator on the right side:
y(1-x) = (1+x)
Step 2: Distributing
Expand the left side of the equation using the distributive property:
y - xy = 1 + x
Step 3: Combining like terms
Rearrange the equation by grouping the terms:
-x + xy - x = 1 - y
Step 4: Factor out x
Factor out x from the left side of the equation:
x(-1 + y - 1) = 1 - y
Step 5: Simplify
Combine the constants on both sides of the equation:
x(y - 2) = 1 - y
Step 6: Divide by (y-2)
Divide both sides of the equation by (y - 2) to isolate x:
x = (1 - y)/(y - 2)
However, based on the desired rearrangement you provided, x = (y-1)/(y+1), it seems there might be an error in your original equation y = (1+x)/(1-x), or the desired rearrangement might be incorrect. Please double-check your equation and the desired rearrangement.