Answer:
The expression simplifies to [tex]\frac{4(x+2)}{5(x-1)}[/tex].
Step-by-step explanation:
The expression
[tex]\frac{2(x+3)}{x(x-1)} *\frac{4x(x+2)}{10(x+3)}[/tex]
can be rearranged and written as
[tex]\frac{8x(x+3)(x+2)}{10x(x-1)(x+3)}.[/tex]
In this form the [tex](x+3)[/tex] terms in the numerator and in the denominator cancel to give
[tex]\frac{8x(x+2)}{10x(x-1)}.[/tex]
The [tex]x's[/tex] are present both in the numerator and in the denominator, so they also cancel, and the fraction [tex]\frac{8}{10}[/tex] simplifies to [tex]\frac{4}{5}[/tex], so finally our expression becomes:
[tex]\boxed{\frac{4(x+2)}{5(x-1)}}[/tex]
Which is our answer:)
