Answers:
Reduce:
Here we gave to simplify the expressions:
9) [tex]x^{2}+7x+\frac{12}{x^{2}}+11x+28[/tex]
Grouping similar terms:
[tex](x^{2}+\frac{12}{x^{2}})+(18x+28)[/tex]
Applying common factor [tex]x^{2}[/tex] in the first parenthesis and common factor [tex]2[/tex] in the second parenthesis:
[tex]x^{2}(1+\frac{12}{x^{4}})+2(9x+14)[/tex] This is the answer
11) [tex]y^{3}+\frac{27}{y^{2}}+2y-3[/tex]
Rearranging the terms:
[tex](y^{3}+2y)+(\frac{27}{y^{2}}-3)[/tex]
Applying common factor [tex]y[/tex] in the first parenthesis and common factor [tex]3[/tex] in the second parenthesis:
[tex]y(y^{2}+2)+3(\frac{9}{y^{2}}-1)[/tex] This is the answer
Multiply:
19) [tex](\frac{12a^{9}u^{7}}{15 c})(\frac{3c^{4}}{21a^{13 u^{8}}})[/tex]
Multiplying both fractions:
[tex]\frac{36 a^{9}u^{7}c^{4}}{315 c a^{13}u^{8}}[/tex]
Dividing numerator and denominator by 3 and simplifying:
[tex]\frac{12 c^{3}}{105 c a^{4}u}[/tex] This is the answer
21) [tex](x-\frac{3}{x}-7)(x^{2}-9x+\frac{35}{x^{2}}-18)[/tex]
[tex](\frac{x^{2}-3-7x}{x})(\frac{x^{4}-9x^{3}+35-18x^{2}}{x^{2}})[/tex]
Operating with cross product:
[tex]x^{2} (x^{2}-3-7x) x(x^{4}-9x^{3}+35-18x^{2})[/tex]
[tex]x^{9} -9x^{8} -18x^{7}+35x^{5}-7x^{8} +63x^{7}+126x^{6}-245x^{4}-3x^{7}+27x^{6}+54x^{5}-105x^{3}[/tex]
Grouping similar terms and factoring:
[tex]x^{9}-2(8x^{8}+21x^{7} )+153x^{6}+89x^{5}-5(49x^{4}+21x^{3})[/tex] This is the answer
Divide:
29) [tex]\frac{\frac{k^{6}}{x^{2}}}{\frac{2k^{4}}{3x^{6}}}[/tex]
[tex]\frac{3k^{6}x^{6}}{2x^{2}k^{4}}[/tex]
Simplifying:
[tex]\frac{3}{2} k^{2}x^{4}[/tex] This is the answer
33) [tex]\frac{\frac{x+5}{x+1}}{\frac{x^{2}+11x+30}{x^{2}+3x+2}}[/tex]
[tex]\frac{(x+5)(x^{2}+3x+2)}{(x+1)(x^{2}+11x+30)}[/tex]
Factoring numerator and denominator:
[tex]\frac{(x+5)(x+2)(x+1)}{(x+1)(x+6)(x+5)}[/tex]
Simplifying:
[tex]\frac{x+2}{x+6}[/tex] This is the answer
37) [tex]\frac{\frac{x-10}{x+13}}{\frac{x^{3}-1000}{x^{2}+15x+21}}[/tex]
[tex]\frac{(x-10)(x^{2}+15x+21)}{(x+13)(x^{3}-1000)}[/tex]
Applying the distributive property in numerator and denominator:
[tex]\frac{x^{3}+15x^{2}+21x-10x^{2}-150x-210}{(x+13)(x^{4}-1000x+13x^{3}-13000)}[/tex]
Grouping similar terms and factoring by common factor:
[tex]-\frac{5x(x^{2}-129)(x^{2}-42)}{1000x^{3} (x+13)(x-13)}[/tex]
Dividing by [tex]5[/tex] in numerator and denominator and simplifying:
[tex]-\frac{(x^{2}-129)(x^{2}-42)}{200x^{2}(x+13)(x-13)}[/tex] This is the answer
