Giải bài 41 trang 53 sách bài tập toán 7 - Cánh diều

Đề bài

Tính:

a) \(\left( {\frac{3}{4}{x^3}} \right):\left( { - \frac{1}{2}{x^2}} \right)\)                                               b) \((5{x^n}):(4{x^2})\) (\(n \in \mathbb{N},n \ge 2\))

c) \(({x^3} - 3{x^2} + 6x):\left( { - \frac{1}{3}x} \right)\)                           d) \(\left( {x + \frac{1}{3}{x^2} + \frac{7}{2}{x^3}} \right):(5x)\)

Lời giải chi tiết

a) \(\left( {\frac{3}{4}{x^3}} \right):\left( { - \frac{1}{2}{x^2}} \right) = \frac{3}{4}:\left( { - \frac{1}{2}} \right).({x^3}:{x^2}) =  - \frac{3}{2}x\)

b) \((5{x^n}):(4{x^2}) = (5:4).({x^n}:{x^2}) = \frac{5}{4}{x^{n - 2}}\)

c) \(({x^3} - 3{x^2} + 6x):\left( { - \frac{1}{3}x} \right) = {x^3}:\left( { - \frac{1}{3}x} \right) - 3{x^2}:\left( { - \frac{1}{3}x} \right) + 6x:\left( { - \frac{1}{3}x} \right)\)

                                     \( = \left[ {1:\left( { - \frac{1}{3}} \right)} \right]({x^3}:x) - \left[ {3:\left( { - \frac{1}{3}} \right)} \right].({x^2}:x) + \left[ {6:\left( { - \frac{1}{3}} \right)} \right].(x:x)\)\( =  - 3{x^2} + 9x - 18\)

d) \(\left( {x + \frac{1}{3}{x^2} + \frac{7}{2}{x^3}} \right):(5x) = x:(5x) + \frac{1}{3}{x^2}:(5x) + \frac{7}{2}{x^3}:(5x)\)

                                   \( = (1:5).(x:x) + \left( {\frac{1}{3}:5} \right).({x^2}:x) + \left( {\frac{7}{2}:5} \right).({x^3}:x)\)

                                   \( = \frac{1}{5} + \frac{1}{{15}}x + \frac{7}{{10}}{x^2} = \frac{7}{{10}}{x^2} + \frac{1}{{15}}x + \frac{1}{5}\)