Bài 7: Phép nhân các phân thức đại số

Có :

\(\left(a^2-bc\right)\left(b-abc\right)=\left(b^2-ac\right)\left(a-abc\right)\)

\(\Leftrightarrow ab\left(a-b\right)+c\left(a^2-b^2\right)=abc^2\left(a-b\right)+abc\left(a^2-b^2\right)\)

\(\Leftrightarrow a^2b-a^3bc-b^2c+ab^2c^2=ab^2-ab^3c-a^2c+a^2bc^2\)

\(\Leftrightarrow ab\left(a-b\right)+c\left(a-b\right)\left(a+b\right)=abc^2\left(a-b\right)+abc\left(a-b\right)\left(a+b\right)\)

\(\Leftrightarrow\left(a-b\right)\left(ab+ac+bc\right)=abc\left(a-b\right)\left(a+b+c\right)\)

Chia 2 vế cho abc(a-b) khác 0 ta được :

\(\left(ab+ac+bc\right):abc=a+b+c\)

\(\Leftrightarrow\dfrac{ab}{abc}+\dfrac{bc}{abc}+\dfrac{ac}{abc}=a+b+c\)

\(\Leftrightarrow\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=a+b+c\left(đpcm\right)\)

\(\dfrac{3x^5+5x^3+1}{4x^4-7x^2+2}.\dfrac{x}{2x+3}.\dfrac{4x^4-7x^2+2}{3x^5+5x^3+1}\) ( sửa đề )

\(=\left[\dfrac{3x^5+5x^3+1}{4x^4-7x^2+2}.\dfrac{4x^4-7x^2+2}{3x^5+5x^3+1}\right].\dfrac{x}{2x+3}\)

\(=\dfrac{x}{2x+3}\)

\(=\dfrac{x}{2x+3}\)

Tóm tắt:

h = 1,2m

d = 10000 N/m³

h_b = 1,2m - 0,65m = 0,55m

a) p_a = ?

b) p_b = ?

Giải

a) Áp suất của nước tác dụng lên điểm a ở đáy bình:

\(p_a=d.h=10000.1,2=12000\) N/m²

b) Áp suất của nước tác dụng lên điểm b cách đáy bình 0,65m:

\(p_b=d.h=10000.0,55=5500\) N/m²

Đáp số: a) p_a = 12000 N/m²

b) p_b = 5500 N/m².

mn ơi, giúp mk nhé!!!

a) Tìm điều kiện xác định A và rút gọc A

b) Tìm x để A = -2

c) Tìm giá trị nhỏ nhất của A

Có:

\(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}=1\)

\(\Rightarrow\left(\dfrac{a}{b+c}+\dfrac{b}{a+c}+\dfrac{c}{a+b}\right).\left(a+b+c\right)=1.\left(a+b+c\right)\)

\(\Rightarrow\dfrac{a\left(a+b+c\right)}{b+c}+\dfrac{b\left(a+b+c\right)}{a+c}+\dfrac{c\left(a+b+c\right)}{a+b}=a+b+c\)

\(\Rightarrow\dfrac{a^2+a\left(b+c\right)}{b+c}+\dfrac{b^2+b\left(a+c\right)}{a+c}+\dfrac{c^2+c\left( a+b\right)}{a+b}=a+b+c\)

\(\Rightarrow\dfrac{a^2}{b+c}+\dfrac{a\left(b+c\right)}{b+c}+\dfrac{b^2}{a+c}+\dfrac{b\left(a+c\right)}{a+c}+\dfrac{c^2}{a+b}+\dfrac{c\left(a+b\right)}{a+b}=a+b+c\)

\(\Rightarrow\dfrac{a^2}{b+c}+a+\dfrac{b^2}{a+c}+b+\dfrac{c^2}{a+b}+c=a+b+c\)

\(\Rightarrow\dfrac{a^2}{b+c}+\dfrac{b^2}{a+c}+\dfrac{c^2}{a+b}=a+b+c-a-b-c\)

\(\Rightarrow\dfrac{a^2}{b+c}+\dfrac{b^2}{a+c}+\dfrac{c^2}{a+b}=0\)

\(\dfrac{a}{x}+\dfrac{b}{y}+\dfrac{c}{z}=0\)

\(\Rightarrow\dfrac{ayz+bxz+cxy}{xyz}=0\)

\(\Rightarrow ayz+bxz+cxy=0\)

\(\dfrac{x}{a}+\dfrac{y}{b}+\dfrac{z}{c}=1\)

\(\Rightarrow\left(\dfrac{x}{a}+\dfrac{y}{b}+\dfrac{z}{c}\right)^2=1\)

\(\Rightarrow\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}+2\left(\dfrac{xy}{ab}+\dfrac{xz}{ac}+\dfrac{yz}{bc}\right)=1\)

\(\Rightarrow\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}+2\left(\dfrac{cxy+bxz+ayz}{abc}\right)=1\)

\(\Rightarrow\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}+2\left(\dfrac{0}{abc}\right)=1\)

\(\Rightarrow\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}+0=1\)

\(\Rightarrow\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}=1\)

Có:

\(\dfrac{a}{x}+\dfrac{b}{y}+\dfrac{c}{z}=0\)

\(\Rightarrow\dfrac{ayz+bxz+cxy}{xyz}=0\)

\(\Rightarrow ayz+bxz+cxy=0\)

Có:

\(\dfrac{x}{a}+\dfrac{y}{b}+\dfrac{z}{c}=1\)

\(\Rightarrow\left(\dfrac{x}{a}+\dfrac{y}{b}+\dfrac{z}{c}\right)^2=1^2\)

\(\Rightarrow\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}+2\left(\dfrac{xy}{ab}+\dfrac{yz}{bc}+\dfrac{xz}{ac}\right)=1\)

\(\Rightarrow\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}+2\left(\dfrac{ayz+bxz+cxy}{abc}\right)=1\)

\(\Rightarrow\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}=1\left(ayz+bxz+cxy=0\right)\)

a,\(A=\left[\dfrac{\left(x-2\right)\left(x+1\right)}{x-1}-\left(x+2\right)\right].\dfrac{x^2-2x+1}{2}\)

A xác định \(\Leftrightarrow x-1\ne0\)

\(\Leftrightarrow x\ne1\)

Rút gọn:

\(A=\left[\dfrac{\left(x-2\right)\left(x+1\right)}{x-1}-\left(x+2\right)\right].\dfrac{\left(x-1\right)^2}{2}\)

\(A=\left[\dfrac{\left(x-2\right)\left(x+1\right)}{x-1}-\dfrac{x+2}{1}\right].\dfrac{\left(x-1\right)^2}{2}\)

\(A=\left[\dfrac{\left(x-2\right)\left(x+1\right)}{x-1}-\dfrac{\left(x+2\right)\left(x-1\right)}{x-1}\right].\dfrac{\left(x-1\right)^2}{2}\)

\(A=\left(\dfrac{x^2-x-2-x^2-x+2}{x-1}\right).\dfrac{\left(x-1\right)^2}{2}\)

\(A=\dfrac{-2}{x-1}.\dfrac{\left(x-1\right)^2}{2}\)

\(A=\dfrac{-2.\left(x-1\right)^2}{\left(x-1\right).2}\)

\(A=-x+1\)

b,\(A=-2\Leftrightarrow-x+1=-2\)

\(\Leftrightarrow-x=-3\)

\(\Leftrightarrow x=3\)