Question

fully simplify the answer and plz explain

Answer 1

Hi there!

$\large\boxed{x = \frac{24z}{(18 + yz)} }$

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:

$\frac{8 * 3 * z}{3xz} - \frac{y * x * z}{3xz} = \frac{6 * 3 * x}{3xz}$

Simplify:

$\frac{24z}{3xz} - \frac{yxz}{3xz} = \frac{18x}{3xz}$

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

$\frac{24z}{3xz} = \frac{18x}{3xz} + \frac{yxz}{3xz}$

Combine fractions:

$\frac{24z}{3xz} = \frac{18x + yxz}{3xz}$

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)

$\frac{24z}{(18 + yz)} = x$