Step 1:
We have to reduce the expression:
[tex]\frac{5xy+x^2}{3x^2+4x}[/tex]
To do that we look at common factors between numerator and denominator, like the factor x:
[tex]\frac{5xy+x^2}{3x^2+4x}=\frac{x\cdot(5y+x)}{x\cdot(3x+4)}=\frac{5y+x}{3x+4}[/tex]
Step 2:
The restricted values of x are the ones that make the rational expression become undefined.
This can happen when the denominator, in this case 3x+4, becomes 0, so we can find the value of x as:
[tex]\begin{gathered} 3x+4=0 \\ 3x=-4 \\ x=-\frac{4}{3} \end{gathered}[/tex]
The restricted value for x is -4/3.
Answer:
The reduced expression is (5y+x)/(3x+4).
The restricted value for x is x = -4/3.
