The answer is: [tex] k^{2} /2
[/tex]
The explanation is shown below:
1. You have the following expression given in the exercise above:
[tex]( 4k^{2}) /(2k+3)(2 k^{2} -5k-12)/(8k-32)
[/tex]
2. By applying the distributive property, you obtain:
[tex] (8k^{4}-20k^{3}-48k)/(16k^{2} -40k-96)[/tex]
3. Now, you must factor [tex] k^{2} [/tex] in the numerator and [tex]2
[/tex] in the denominator:
[tex] k^{2}(8 k^{2} -20k-48)/2(8 k^{2} -20k-48)[/tex]
4. Simplify:
[tex] k^{2} /2[/tex]
