Question

Solve for x: 1/x+4 - 1/x-7 =11/30 ;x is not equal to -4, 7

Answer 1

Answer:

2 or 1

Step-by-step explanation:

= > 1/(x + 4) - 1/(x - 7) = 11/30

= > { (x - 7) - (x + 4) }/(x+4)(x-7) = 11/30

= > 30 { x - 7 - x - 4 } = 11( x + 4 )( x - 7 )

= > 30( - 11 ) = 11( x² - 7x + 4x - 28 )

= > - 30(11) = 11( x² - 3x - 28 )

= > - 30 = x² - 3x - 28

= > x² - 3x + 30 - 28 = 0

= > x² - 3x + 2 = 0

= > x² - 2x - x + 2 = 0

= > x( x - 2 ) - ( x - 2 ) = 0

= > ( x - 2 )( x - 1 ) = 0

= > x = 2 or 1

Answer 2

$\huge\star\bold\gray{Hello!}$

$\large\sf\red{\frac{1}{x + 4} - \frac{1}{x - 7} = \frac{11}{30}}$

$\longrightarrow$$\small\sf\red{\frac{(x - 7) - (x + 4)}{(x + 4)(x - 7)} = \frac{11}{30} }$

$\longrightarrow$$\small\sf\red{ \frac{x - 7 - x - 4}{ {x}^{2} - 7x + 4 x - 28 } = \frac{11}{30} }$

$\longrightarrow$$\small\sf\red{\frac{ - 11}{ {x}^{2} - 3x - 28 } = \frac{11}{30} }$

$\longrightarrow$$\small\sf\red{ \frac{ - 1}{ {x}^{2} - 3x - 28} = \frac{1}{30} }$

$\longrightarrow$$\small\sf\red{- {x}^{2} - 3x + 28 = 30}$

$\longrightarrow$$\small\sf\red{ - {x}^{2} - 3x + 28 - 30 = 0 }$

$\longrightarrow$$\small\sf\red{- {x}^{2} - 3x + 2 = 0}$

$\longrightarrow$$\small\sf\red{{x}^{2} - 3x + 2 = 0}$

$\longrightarrow$$\small\sf\red{ {x}^{2} - 2x - x + 2 = 0}$

$\longrightarrow$$\small\sf\red{x(x - 2) - 1(x - 2) = 0}$

$\longrightarrow$$\small\sf\red{(x-1)(x-2)=0}$

⠀⠀

$\longrightarrow$$\small\sf\red{x-1=0,x=1}$

$\longrightarrow$$\small\sf\red{x-2=0,x=2}$