What is the answer to (z+a)/(a-b)+(z-a)/(a+b)=(z+b)/(a+b)-(z-b)/(a-b) ?

The answer to (z+a)/(a-b)+(z-a)/(a+b)=(z+b)/(a+b)-(z-b)/(a-b) is z=0;\quad (a-b)(a+b)\ne 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(z+a)/(a-b)+(z-a)/(a+b)=(z+b)/(a+b)-(z-b)/(a-b)

\frac{z + a}{a - b} + \frac{z - a}{a + b} = \frac{z + b}{a + b} - \frac{z - b}{a - b}

z = 0; (a - b) (a + b) \neq = 0

Solution steps

\frac{z + a}{a - b} + \frac{z - a}{a + b} = \frac{z + b}{a + b} - \frac{z - b}{a - b}

Multiply by LCM

(z + a) (a + b) + (z - a) (a - b) = (z + b) (a - b) - (z - b) (a + b); (a - b) (a + b) \neq = 0

Expand

(z + a) (a + b) + (z - a) (a - b) : 2 a z + 2 ab

Expand

(z + b) (a - b) - (z - b) (a + b) : - 2 b z + 2 ab

2 a z + 2 ab = - 2 b z + 2 ab; (a - b) (a + b) \neq = 0

Move

2 ab

to the right side

2 a z = - 2 b z; (a - b) (a + b) \neq = 0

Move

2 b z

to the left side

2 a z + 2 b z = 0; (a - b) (a + b) \neq = 0

Factor

2 a z + 2 b z : 2 z (a + b)

2 z (a + b) = 0; (a - b) (a + b) \neq = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

z = 0; (a - b) (a + b) \neq = 0

y, x = 2 y - 3

x, x + y = 30

6 - 5 x + 2 x = 8 - 4 x

12 a - 16 a = - 8

x, 2 x + 5 y = 12

What is the answer to (z+a)/(a-b)+(z-a)/(a+b)=(z+b)/(a+b)-(z-b)/(a-b) ?
The answer to (z+a)/(a-b)+(z-a)/(a+b)=(z+b)/(a+b)-(z-b)/(a-b) is z=0;\quad (a-b)(a+b)\ne 0