\(\Leftrightarrow\frac{6x+5}{12x+9}-\frac{3x-7}{12x-9}=\frac{4x^2+10x-7}{16x^2-9}.\)

\(\Leftrightarrow\frac{\left(6x+5\right)\left(12x-9\right)-\left(3x-7\right)\left(12x+9\right)}{\left(3.4.x\right)^2-\left(3.3\right)^2}=\frac{4x^2+10x-7}{16x^2-9}\)

\(\Leftrightarrow\frac{72x^2+6x-45-\left(36x^2-57x-63\right)}{3^2\left(16x^2-9\right)}=\frac{4x^2+10x-7}{16x^2-9}\)

ĐK: \(16x^2-9\ne0\Leftrightarrow x^2\ne\left(\frac{3}{4}\right)^2\Rightarrow x\ne\pm\frac{3}{4}\)

\(\Leftrightarrow72x^2+6x-45-36x^2+57x+63=36x^2+90x-63\)

\(\Leftrightarrow27x=81\Leftrightarrow x=3\)

a) A = x²(m + 5) - x(m + 5)(x + 3/2) + (x - m)

A = mx² + 5x² - mx² - 3/2mx - 5x² - 15/2x + x - m

A = -3/2mx - m - 13/2x

b) Khi m = -1, ta có: 

(-3/2).(-1).x - (-1) - 13/2x = 0

<=> 3/2x - 13/2x + 1 = 0

<=> 3/2x - 13/2x = 0 - 1

<=> 3/2x - 13/2x = -1

<=> 3x - 13x = -2

<=> -10x = -2

<=> x = -2/-10 = 1/5

9) bài này nhiều cách thay lắm. chả biết cách nào nhanh hơn. 

ĐK : ...

\(N=\frac{a+x+1}{a+x}:\frac{a^2+ax-a}{a+x}.\left[\frac{2ax-1+\left(a^2+x^2\right)}{2ax}\right]\)

\(N=\frac{a+x+1}{a+x}.\frac{a+x}{a\left(a+x-1\right)}.\frac{\left(a+x\right)^2-1}{2ax}\)

\(N=\frac{a+x+1}{a\left(a+x-1\right)}.\frac{\left(a+x-1\right)\left(a+x+1\right)}{2ax}\)

\(N=\frac{\left(a+x+1\right)^2}{2a^2x}=\frac{\left(a+1+\frac{1}{a-1}\right)^2}{\frac{2a^2}{a-1}}\)

\(N=\frac{\left(\frac{\left(a+1\right)\left(a-1\right)+1}{a-1}\right)^2}{\frac{2a^2}{a-1}}=\frac{\left(\frac{a^2}{a-1}\right)^2}{\frac{2a^2}{a-1}}=\frac{\frac{a^4}{\left(a-1\right)^2}}{\frac{2a^2}{a-1}}=\frac{a^2}{2\left(a-1\right)}\)

10) \(3a^2+3b^2=10ab\Leftrightarrow3a^2-10ab+3b^2=0\)

\(\Leftrightarrow\left(3a^2-9ab\right)-\left(ab-3b^2\right)=0\)

\(\Leftrightarrow3a\left(a-3b\right)-b\left(a-3b\right)=0\)

\(\Leftrightarrow\left(3a-b\right)\left(a-3b\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}3a=b\\a=3b\left(loai-vi-b>a>0\right)\end{cases}}\)

Thay 3a = b vào biểu thức, ta có :

\(P=\frac{a-b}{a+b}=\frac{a-3a}{a+3a}=\frac{-2a}{4a}=\frac{-1}{2}\)

Gọi số nhà của An là ab 

Theo đề bài. ta có:

=> 6ab - ab6 = 162

=> 600 + ab - 10ab - 6 = 162

=> 594 - 9ab = 162

=> 9ab = 432

=> ab = 48

Vậy số nhà của An là 48

Theo giả thiết: \(x+\frac{1}{x}=3\left(x\ne0\right)\)

\(\Rightarrow\left(x+\frac{1}{x}\right)^2=9\)

\(\Rightarrow x^2+2+\frac{1}{x^2}=9\)

\(\Rightarrow x^2+\frac{1}{x^2}=7\)

\(\Rightarrow A=x^2+\frac{1}{x^2}-\frac{1}{2}=7-\frac{1}{2}=\frac{13}{2}\)

Vậy \(A=\frac{13}{2}\)

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