Question

Can someone actually show me how to solve this, and not give me just the answer? See attached picture.

Answer 1

(1)/(a)=(1)/(s)+(1)/(y)

Since y is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
(1)/(s)+(1)/(y)=(1)/(a)

Since (1)/(s) does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting (1)/(s) from both sides.
(1)/(y)=-(1)/(s)+(1)/(a)

Simplify the right-hand side of the equation.
(1)/(y)=(-a+s)/(as)

Since there is one rational expression on each side of the equation, this can be solved as a ratio. For example, (A)/(B)=(C)/(D) is equivalent to A*D=B*C.
1*as=(-a+s)*y

Since y is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
(-a+s)*y=1*as

Multiply (-a+s) by y to get y(-a+s).
y(-a+s)=1*as

Multiply 1 by as to get as.
y(-a+s)=as

Multiply y by each term inside the parentheses.
-ay+sy=as

Factor out the GCF of -y from each term in the polynomial.
-y(a)-y(-s)=as

Factor out the GCF of -y from -ay+sy.
-y(a-s)=as

Divide each term in the equation by (a-s).
-(y(a-s))/(a-s)=(as)/(a-s)

Simplify the left-hand side of the equation by canceling the common factors.
-y=(as)/(a-s)

Multiply each term in the equation by -1.
-y*-1=(as)/(a-s)*-1

Multiply -y by -1 to get y.
y=(as)/(a-s)*-1

Simplify the right-hand side of the equation by simplifying each term.
y=-(as)/(a-s)

Answer 2

in english:
1) subtract
\[\frac{1}{s}\] from both sides.
2) take the reciprocal

Answer 3

\[\Large \frac{1}{A}=\frac{1}{s}+\frac{1}{y}\]


\[\Large sy=Ay+As\]


\[\Large sy-Ay=As\]


\[\Large y(s-A)=As\]


\[\Large y=\frac{As}{s-A}\]

Note: in the second step, I multiplied EVERY term by the LCD Asy

Answer 4

you get
\[\frac{1}{A}-\frac{1}{s}=\frac{s-A}{sA}=\frac{1}{y}\] so
\[y=\frac{sA}{s-A}\]

Answer 5

My mind can't grasp how to do these problems, no matter how many I do. I keep getting stuck after I subtract the 1/s to get 1/y alone.

Answer 6

just multiply every term by the LCD to clear out the fractions

Answer 7

jimthomson has one way, i wrote another. which ever you prefer. if the fractions don't bother you then subtract
\[\frac{1}{A}-\frac{1}{s}=\frac{s-A}{sA}\] just like you would with
\[\frac{1}{3}-\frac{1}{4}\]
if they bother you, then clear them (carefully)

Answer 8

I just tried another example, like this one and got it right!! Thank you both guys! You have no idea how much you just helped me!