Solve the literal equation for a
y=x(ab/a-b)
Hi Helen, this is easy!
Solving the literal equation for 'a' means expressing the equation in terms of a.
Let us see the solutions step by step:
a) Multiplying the denominator a-b with y gives : y(a-b) = xab
b)Expanding the parentheses y(a-b) gives ya-yb = xab
c)Since ya and xab have 'a', the equation is now rearranged as:
ya-xab = yb
d)Taking out the 'a' from ya-xab
ya-xab = a(y-xb)
e) a(y-xb) = yb
a = yb/(y-xb)---> final answer
Well, that equation looks a bit complex, but I'll give it a shot! Let's solve it for "a." Here we go:
First, let's simplify the equation a bit:
y = x(ab / (a - b))
To get rid of the denominator, we can multiply both sides of the equation by (a - b):
y(a - b) = x(ab / (a - b))(a - b)
Expanding the left side:
ya - yb = xab
To isolate "a," let's swap the terms around:
ya = xab + yb
Next, we can factor out the common factor of "a" on the right side:
ya = a(xb + yb)
Now, let's divide both sides of the equation by (xb + yb) to solve for "a":
ya / (xb + yb) = a
And there you have it! The solution for "a" is a = ya / (xb + yb). Hope that brings a smile to your face!
To solve the literal equation for "a", we will isolate the variable "a" on one side of the equation.
Step 1: Distribute the "x" term to both terms within the parentheses:
y = x(ab/a - b) - Distribute the "x" to both terms within the parentheses
y = x(ab/a) - xb
Step 2: Simplify the term "ab/a":
The term "ab/a" simplifies to "b", as the "a" in the numerator cancels out with the "a" in the denominator.
y = xb - xb - Simplify ab/a to b
y = 0
Step 3: Isolate "a" on one side of the equation:
To isolate "a", we need to express "xb" on the right side of the equation as a common factor.
y = xb - xb (Rearrange the equation)
y = xb(1 - 1) (Factor out "xb")
y = xb(0) (Simplify 1 - 1 to 0)
y = 0
Step 4: Solve for "a":
Since the equation simplifies to "0 = 0", there is no specific value for "a". The equation is satisfied for any value of "a". Therefore, "a" can take on any real number.
Hence, the solution to the literal equation for "a" is "a can be any real number".
To solve the literal equation for "a" in terms of "x" and "y," we need to isolate "a" on one side of the equation. Let's go step by step:
1. Start with the equation: y = x(ab/a-b)
2. Remove the parentheses by distributing the x on the right side of the equation:
y = xab/(a-b)
3. Multiply both sides of the equation by (a-b) to eliminate the denominator on the right side:
y(a-b) = xab
4. Expand the left side of the equation:
ya - yb = xab
5. Distribute the y on the left side:
ya - yb = axb
6. Rearrange the terms to isolate "a" on one side:
axb = ya - yb
7. Divide both sides of the equation by xb to solve for "a":
a = (ya - yb)/xb
Therefore, the solution for "a" in terms of "x" and "y" is:
a = (ya - yb)/xb