Algebra Question! Please Help! Solve for z:

Question

Solve for z:

(a/z)+(y/a)=x

(A) (a)/(x-y)

(B) a(ax+y)/(xy)

(C) (a²)/(ax-y)

(D) (a)/(ax+y)

(E) none of these

Answer 1

The answer is C.

Solution: Adding fractions with different denominators, you should make them the same.

Step 1) First fraction a/z is multiplied by a/a, and second fraction y/a is multiplied by z/z, so you will have (a^2+yz)/az = x.

Step 2) Opposite of division is multiplication, so when you times both sides by az of the equation your answer will be a^2+yz=xaz. The question says solve for z, so you need to make the z alone.

Step 3) Rearrange the formula. Put all z terms on one side of the equation. xaz-yz=a^2

Step 4) Put z outside of the paranthesis z(xa-y)=a^2

Step 5) There is an invisible times sign between z and the paranthesis, so opposite of times(multiplication) is division. When you divide both sides by (xa-y), your answer will be z=a^2/(xa-y) or you can write it as z=a^2/(ax-y).

Answer 2

(a/z)+(y/a)=x

(a/z)=x-(y/a)

(a/z)=(ax/a)-(y/a)

(a/z)=(ax-y)/a

take the reciprocal of both sides

(z/a)=a/(ax-y)

multiply both sides by "a"

z=(a^2)/(ax-y) which is (C)