Question

The following rational equation has denominators that contain variables. For this​ equation,
a. Write the value or values of the variable that make a denominator zero. These are the restrictions on the variable.
b. Keeping the restrictions in​ mind, solve the equation. StartFraction 9 Over 5 x plus 5 EndFraction equals StartFraction 6 Over x plus 1 EndFraction minus three fifths 9 5x+5 = 6 x+1 − 3 5
What​ is/are the value or values of the variable that​ make(s) the denominators​ zero?

Answer 1

Part a: The restrictions on the variable x is x=0

Part b: The solution of the equation is $x=\frac{21}{23}$

Explanation:

The equation is $\frac{9}{5x} +5=\frac{6}{x} +1-\frac{3}{5}$

Part a:

The restriction of a variable that makes the denominator equal to zero.

Thus, the variable that makes the equation's denominator equal to zero is x=0

Part b:

To solve the equation

$\frac{9}{5x} +5=\frac{6}{x} +1-\frac{3}{5}$

Subtracting both sides by $\frac{6}{x}$ and 5, we get,

$\frac{9}{5x} -\frac{6}{x} =1-5-\frac{3}{5}$

Taking LCM,

$\frac{9-30}{5x} =\frac{5-25-3}{5}$

Simplifying,

$\frac{-21}{5x} =\frac{-23}{5}$

$21=23x$

Dividing both sides by 23,

$x=\frac{21}{23}$

Thus, the solution of the equation is $x=\frac{21}{23}$