Answer: d) No solution.
Step-by-step explanation:
Given the equation:
[tex]\frac{3}{2}=\frac{3x}{2x}-\frac{6}{5x}[/tex]
The denominator of the fractions cannot be zero, then, the Domain is:
[tex]x\neq 0[/tex]
Simplify:
[tex]\frac{3}{2}=\frac{3}{2}-\frac{6}{5x}[/tex]
Subtract [tex]\frac{3}{2}[/tex] from both sides of the equation. Then you get:
[tex]\frac{3}{2}-(\frac{3}{2})=\frac{3}{2}-\frac{6}{5x}-(\frac{3}{2})\\\\0=-\frac{6}{5x}[/tex]
Multiply both sides of the equation by [tex]5x[/tex] ([tex]5x \neq 0[/tex]), then:
[tex](5x)(0)=(-\frac{6}{5x})(5x)[/tex]
Since the multiplication of [tex]5x[/tex] by zero is zero, you get:
[tex]0=-6[/tex] (This is FALSE)
Therefore, since there is no value for the variable that makes the equation true, the equation has NO SOLUTION.
