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Exercise

y=x(x3−5)x+3y=\frac{x\left(x^3-5\right)}{\sqrt{x+3}}

Step-by-step Solution

1

Factor the difference of cubes: a3−b3=(a−b)(a2+ab+b2)a^3-b^3 = (a-b)(a^2+ab+b^2)

y=x(x−53)(x2+53x+(5)23)x+3y=\frac{x\left(x-\sqrt[3]{5}\right)\left(x^2+\sqrt[3]{5}x+\sqrt[3]{\left(5\right)^{2}}\right)}{\sqrt{x+3}}

Final answer to the exercise

y=x(x−53)(x2+53x+(5)23)x+3y=\frac{x\left(x-\sqrt[3]{5}\right)\left(x^2+\sqrt[3]{5}x+\sqrt[3]{\left(5\right)^{2}}\right)}{\sqrt{x+3}}

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y=x(x3−5)√x+3 
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