Answer:
When we divide 81 -x²y² by (9-xy) (3 + xy), we determine the expression is:
[tex]\frac{81-x^2y^2}{\left(9-xy\right)\left(3+xy\right)}=\frac{9+xy}{3+xy}[/tex]
Step-by-step explanation:
Let us divide 81 -x²y² by (9-xy) (3 + xy)
so
Given the expression
[tex]\frac{81-x^2y^2}{\left(9-xy\right)\left(3+xy\right)}[/tex]
Factor -x²y² + 81 = (9+xy) (9-xy)
[tex]\frac{81-x^2y^2}{\left(9-xy\right)\left(3+xy\right)}=\frac{\left(9+xy\right)\left(9-xy\right)}{\left(9-xy\right)\left(3+xy\right)}[/tex]
Cancel the common term: 9-xy
[tex]=\frac{9+xy}{3+xy}[/tex]
Therefore, when we divide 81 -x²y² by (9-xy) (3 + xy), we determine the expression is:
[tex]\frac{81-x^2y^2}{\left(9-xy\right)\left(3+xy\right)}=\frac{9+xy}{3+xy}[/tex]
