ax/b + cx/d =e
solve for variable x
ax/b + cx/d = e
Multiply both sides by bd
adx + bcx = bde
x(ad + bc) = bde
x = bde/(ad + bc)
Indicate ax+b=c*x+d for d
I don’t know
Ah, the mathematical equation! Trying to solve it, are we? Well, fear not! I, the Clown Bot, am here to assist you. Let's get ready for some fun with numbers!
Now, to solve the equation ax/b + cx/d = e for the variable x, we need to get rid of those pesky denominators. To do that, we'll cross multiply:
(ad)(ax) + (bc)(cx) = (be)(bd)
Now, let's simplify and combine like terms:
a^2xd + b^2xc^2 = bed^2
Finally, let's isolate x:
x(a^2d + b^2c^2) = bed^2
Now, finishing off, we can divide both sides by (a^2d + b^2c^2):
x = bed^2 / (a^2d + b^2c^2)
There you have it! The solution for x is bed^2 divided by (a^2d + b^2c^2). Remember, math can be quite entertaining with the right mindset. Keep smiling, my friend!
To solve the equation ax/b + cx/d = e for the variable x, follow these steps:
Step 1: Clear the fractions
To eliminate the fractions in the equation, we can start by multiplying every term of the equation by the least common multiple (LCM) of b and d. The LCM of b and d can be found by multiplying the individual prime factors with their highest exponent.
LCM(b, d) = (prime factors of b) x (prime factors of d)
Step 2: Expand the equation
After multiplying each term by the LCM, the equation becomes:
(ax/b) * LCM(b, d) + (cx/d) * LCM(b, d) = e * LCM(b, d)
Step 3: Simplify the equation
Simplify each term:
(ax/b) * (d * LCM(b, d)/d) + (cx/d) * (b * LCM(b, d)/b) = e * LCM(b, d)
This simplifies to:
(axd)/d + (cxb)/b = e * LCM(b, d)
Simplified equation:
(axd + cxb)/d = e * LCM(b, d)
Step 4: Solve for x
To solve for x, we need to isolate x. Multiply both sides of the equation by d to get rid of the fraction:
axd + cxb = e * LCM(b, d) * d
Next, move the term cxb to the other side of the equation:
axd = -cxb + e * LCM(b, d) * d
Factor out x on the left-hand side:
x(ad - c*b) = e * LCM(b, d) * d
Finally, divide both sides of the equation by (ad - cb) to solve for x:
x = (e * LCM(b, d) * d) / (ad - cb)
This is the solution for x in terms of the other variables and constants in the equation.