What is the domain of y=(4x+1)/(2x+3)-(3x+2)/(5x-1) ?

The domain of y=(4x+1)/(2x+3)-(3x+2)/(5x-1) is x 1/5

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domain of y=(4x+1)/(2x+3)-(3x+2)/(5x-1)

domain

y = \frac{4 x + 1}{2 x + 3} - \frac{3 x + 2}{5 x - 1}

x < - \frac{3}{2} or - \frac{3}{2} < x < \frac{1}{5} or x > \frac{1}{5}

Interval Notation

(- \infty, - \frac{3}{2}) \cup (- \frac{3}{2}, \frac{1}{5}) \cup (\frac{1}{5}, \infty)

Solution steps

Find undefined (singularity) points:

x = - \frac{3}{2}, x = \frac{1}{5}

The function domain

x < - \frac{3}{2} or - \frac{3}{2} < x < \frac{1}{5} or x > \frac{1}{5}

\frac{( x ^{2} - 3 x + 2 )}{x ^{2} + x - 6}

\frac{( x - 3 ) ^{2}}{2}

g (x) = lo g_{10} (x - x^{2})

ln (16 - y^{2})

\frac{x + 6}{- 4 x}

What is the domain of y=(4x+1)/(2x+3)-(3x+2)/(5x-1) ?
The domain of y=(4x+1)/(2x+3)-(3x+2)/(5x-1) is x<-3/2 \lor-3/2 <x< 1/5 \lor x> 1/5