Question

Fully simplify the answer and plz explain

Answer 1

Hi there!

`\large\boxed{x = (24z)/((18 + yz)) }`

We can begin solving by creating a common denominator:

x · 3 · z = 3xz. This is the denominator that all of the numerators must have in order to work with the fractions.

Multiply each numerator by the missing parts of the common denominator:

`(8 * 3 * z)/(3xz) - (y * x * z)/(3xz) = (6 * 3 * x)/(3xz)`

Simplify:

`(24z)/(3xz) - (yxz)/(3xz) = (18x)/(3xz)`

Move all the fractions involving x in the numerator to the right-hand side of the equation:

`(24z)/(3xz) = (18x)/(3xz) + (yxz)/(3xz)`

Combine fractions:

`(24z)/(3xz) = (18x + yxz)/(3xz)`

Multiply both sides by 3xz:

`24z = 18x + yxz`

Factor out "x" from the terms on the right-hand side:

`24z = x(18 + yz)`

Divide both sides by (18 + yz)

`(24z)/((18 + yz)) = x`