Question

If you could show as much work as possible that would be amazing!!

Answer 1

Answers:

Reduce:

Here we gave to simplify the expressions:

9) $x^{2}+7x+\frac{12}{x^{2}}+11x+28$

Grouping similar terms:

$(x^{2}+\frac{12}{x^{2}})+(18x+28)$

Applying common factor $x^{2}$ in the first parenthesis and common factor $2$ in the second parenthesis:

$x^{2}(1+\frac{12}{x^{4}})+2(9x+14)$ This is the answer

11) $y^{3}+\frac{27}{y^{2}}+2y-3$

Rearranging the terms:

$(y^{3}+2y)+(\frac{27}{y^{2}}-3)$

Applying common factor $y$ in the first parenthesis and common factor $3$ in the second parenthesis:

$y(y^{2}+2)+3(\frac{9}{y^{2}}-1)$ This is the answer

Multiply:

19) $(\frac{12a^{9}u^{7}}{15 c})(\frac{3c^{4}}{21a^{13 u^{8}}})$

Multiplying both fractions:

$\frac{36 a^{9}u^{7}c^{4}}{315 c a^{13}u^{8}}$

Dividing numerator and denominator by 3 and simplifying:

$\frac{12 c^{3}}{105 c a^{4}u}$ This is the answer

21) $(x-\frac{3}{x}-7)(x^{2}-9x+\frac{35}{x^{2}}-18)$

$(\frac{x^{2}-3-7x}{x})(\frac{x^{4}-9x^{3}+35-18x^{2}}{x^{2}})$

Operating with cross product:

$x^{2} (x^{2}-3-7x) x(x^{4}-9x^{3}+35-18x^{2})$

$x^{9} -9x^{8} -18x^{7}+35x^{5}-7x^{8} +63x^{7}+126x^{6}-245x^{4}-3x^{7}+27x^{6}+54x^{5}-105x^{3}$

Grouping similar terms and factoring:

$x^{9}-2(8x^{8}+21x^{7} )+153x^{6}+89x^{5}-5(49x^{4}+21x^{3})$ This is the answer

Divide:

29) $\frac{\frac{k^{6}}{x^{2}}}{\frac{2k^{4}}{3x^{6}}}$

$\frac{3k^{6}x^{6}}{2x^{2}k^{4}}$

Simplifying:

$\frac{3}{2} k^{2}x^{4}$ This is the answer

33) $\frac{\frac{x+5}{x+1}}{\frac{x^{2}+11x+30}{x^{2}+3x+2}}$

$\frac{(x+5)(x^{2}+3x+2)}{(x+1)(x^{2}+11x+30)}$

Factoring numerator and denominator:

$\frac{(x+5)(x+2)(x+1)}{(x+1)(x+6)(x+5)}$

Simplifying:

$\frac{x+2}{x+6}$ This is the answer

37) $\frac{\frac{x-10}{x+13}}{\frac{x^{3}-1000}{x^{2}+15x+21}}$

$\frac{(x-10)(x^{2}+15x+21)}{(x+13)(x^{3}-1000)}$

Applying the distributive property in numerator and denominator:

$\frac{x^{3}+15x^{2}+21x-10x^{2}-150x-210}{(x+13)(x^{4}-1000x+13x^{3}-13000)}$

Grouping similar terms and factoring by common factor:

$-\frac{5x(x^{2}-129)(x^{2}-42)}{1000x^{3} (x+13)(x-13)}$

Dividing by $5$ in numerator and denominator and simplifying:

$-\frac{(x^{2}-129)(x^{2}-42)}{200x^{2}(x+13)(x-13)}$ This is the answer