What is the answer to solvefor x, x/((2+z))= x/2+x/z ?

The answer to solvefor x, x/((2+z))= x/2+x/z is x=0;\quad z\ne 0,z\ne-2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

solvefor x, x/((2+z))= x/2+x/z

solve for

x, \frac{x}{( 2 + z )} = \frac{x}{2} + \frac{x}{z}

x = 0; z \neq = 0, z \neq = - 2

Solution steps

\frac{x}{( 2 + z )} = \frac{x}{2} + \frac{x}{z}

Multiply by LCM

2 x z = x z (z + 2) + 2 x (z + 2); z \neq = 0, z \neq = - 2

Expand

x z (z + 2) : x z^{2} + 2 x z

2 x z = x z^{2} + 2 x z + 2 x (z + 2)

Expand

2 x (z + 2) : 2 x z + 4 x

2 x z = x z^{2} + 2 x z + 2 x z + 4 x

Add similar elements:

2 x z + 2 x z = 4 x z

2 x z = x z^{2} + 4 x z + 4 x; z \neq = 0, z \neq = - 2

Subtract

x z^{2} + 4 x z + 4 x

from both sides

2 x z - (x z^{2} + 4 x z + 4 x) = x z^{2} + 4 x z + 4 x - (x z^{2} + 4 x z + 4 x); z \neq = 0, z \neq = - 2

Simplify

- x z^{2} - 2 x z - 4 x = 0; z \neq = 0, z \neq = - 2

Factor

- x z^{2} - 2 x z - 4 x : - x (z^{2} + 2 z + 4)

- x (z^{2} + 2 z + 4) = 0; z \neq = 0, z \neq = - 2

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0; z \neq = 0, z \neq = - 2

2 + 3 x = 62

\frac{4 x}{3} = 26

2 - \frac{1}{3} x = \frac{1}{6} x + 1

6 - 4 x = 6 x - 8 x + 4

15 x - (3 x - 3) = 5 - 4 x

What is the answer to solvefor x, x/((2+z))= x/2+x/z ?
The answer to solvefor x, x/((2+z))= x/2+x/z is x=0;\quad z\ne 0,z\ne-2