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a)
\(\frac{x^2-16}{4x-x^2}=\frac{x^2-4^2}{x(4-x)}=\frac{(x-4)(x+4)}{x(4-x)}=\frac{x+4}{-x}\)
b) \(\frac{x^2+4x+3}{2x+6}=\frac{x^2+x+3x+3}{2(x+3)}=\frac{x(x+1)+3(x+1)}{2(x+3)}=\frac{(x+1)(x+3)}{2(x+3)}=\frac{x+1}{2}\)
c)
\(\frac{15x(x+y)^3}{5y(x+y)^2}=\frac{5.3.x(x+y)^2.(x+y)}{5y(x+y)^2}=\frac{3x(x+y)}{y}\)
d) \(\frac{5(x-y)-3(y-x)}{10(x-y)}=\frac{5(x-y)+3(x-y)}{10(x-y)}=\frac{8(x-y)}{10(x-y)}=\frac{8}{10}=\frac{4}{5}\)
e) \(\frac{2x+2y+5x+5y}{2x+2y-5x-5y}=\frac{7x+7y}{-3x-3y}=\frac{7(x+y)}{-3(x+y)}=\frac{-7}{3}\)
f) \(\frac{x^2-xy}{3xy-3y^2}=\frac{x(x-y)}{3y(x-y)}=\frac{x}{3y}\)
g) \(\frac{2ax^2-4ax+2a}{5b-5bx^2}=\frac{2a(x^2-2x+1)}{5b(1-x^2)}=\frac{2a(x-1)^2}{5b(1-x)(1+x)}\)
\(=\frac{2a(x-1)}{5b(-1)(x+1)}=\frac{2a(1-x)}{5b(x+1)}\)
Ta có \(6a^2-15ab+5b^2=0\Leftrightarrow15ab=6a^2+5b^2\)
\(Q=\dfrac{\left(2a-b\right)\left(3a+b\right)+\left(5b-a\right)\left(3a-b\right)}{9a^2-b^2}\)
\(Q=\dfrac{3a^2+15ab-6b^2}{9a^2-b^2}=\dfrac{3a^2+6a^2+5b^2-6b^2}{9a^2-b^2}\)
\(Q=\dfrac{9a^2-b^2}{9a^2-b^2}=1\)
1 ) \(A=\left(\dfrac{2x^3+2}{x+1}-2x\right)\left(\dfrac{x^3-1}{x-1}+x\right)\)
\(\Leftrightarrow A=\left(\dfrac{2x^3+2-2x^2-2x}{x+1}\right)\left(x^2+2x+1\right)\)
\(\Leftrightarrow A=\left(\dfrac{\left(2x^2-2\right)\left(x-1\right)}{x+1}\right)\left(x+1\right)^2\)
\(\Leftrightarrow A=\left(\dfrac{2\left(x-1\right)\left(x+1\right)\left(x-1\right)}{x+1}\right)\left(x+1\right)^2\)
\(\Leftrightarrow A=2\left(x-1\right)^2\left(x+1\right)^2\ge0\forall x\)
Lời giải:
Vì \(2a-b=5\Rightarrow b=2a-5\Rightarrow 2b=4a-10\)
\(\Rightarrow 7a-2b=7a-(4a-10)=3a+10\)
\(\Rightarrow \frac{7a-2b}{3a+10}=\frac{3a+10}{3a+10}=1\)
Lại có:
\(2a-b=5\Rightarrow 2a=b+5\Rightarrow 4a=2b+10\)
\(\Rightarrow 7b-4a=7b-(2b+10)=5b-10\)
\(\Rightarrow \frac{7b-4a}{15b-30}=\frac{5b-10}{15b-30}=\frac{5b-10}{3(5b-10)}=\frac{1}{3}\)
Vậy: \(A=1-\frac{1}{3}=\frac{2}{3}\)
ta có : \(x+3+\dfrac{4-3a^2}{a^2-9}=\dfrac{5}{2a^2+6a}\)
\(\Leftrightarrow x+3=\dfrac{5}{2a^2+6a}-\dfrac{4-3a^2}{a^2-9}\)
\(\Leftrightarrow x+3=\dfrac{5}{2a\left(a+3\right)}-\dfrac{4-3a^2}{\left(a+3\right)\left(a-3\right)}\) \(\Leftrightarrow x+3=\dfrac{5\left(a-3\right)-2a\left(4-3a^2\right)}{2a\left(a+3\right)\left(a-3\right)}\) \(\Leftrightarrow x+3=\dfrac{5a-15-8a+6a^3}{2a\left(a+3\right)\left(a-3\right)}=\dfrac{6a^3-3a-15}{2a\left(a+3\right)\left(a-3\right)}\)\(\Leftrightarrow x=\dfrac{6a^3-3a-15}{2a\left(a+3\right)\left(a-3\right)}-3=\dfrac{6a^3-3a-15-3.2a\left(a^2-9\right)}{2a\left(a+3\right)\left(a-3\right)}\)
\(\Leftrightarrow x=\dfrac{6a^3-3a-15-6a^3+54a}{2a\left(a+3\right)\left(a-3\right)}=\dfrac{51a-15}{2a\left(a^2-9\right)}\)
Bác làm nhanh ***** :((