a)

\(\frac{x}{3}-\frac{5x}{6}-\frac{15x}{12}=\frac{x}{4}-5\)

\(\Leftrightarrow\frac{4x-10x-15x}{12}=\frac{3x-60}{12}\)

\(\Leftrightarrow\frac{-10x-11}{12}=\frac{3x-60}{12}\)

\(\Leftrightarrow\frac{-10x-11-3x+60}{12}=0\)

\(\Leftrightarrow\frac{49-13x}{12}=0\)

\(\Rightarrow49-13x=0\)

\(\Rightarrow x=\frac{-49}{13}\)

b)

\(\frac{8x-3}{4}-\frac{3x-2}{2}=\frac{2x-1}{2}+\frac{x+3}{4}\)

\(\Leftrightarrow\frac{8x-3-6x+4}{4}=\frac{4x-2+x+3}{4}\)

\(\Leftrightarrow\frac{2x+1}{4}=\frac{5x+1}{4}\)

\(\Leftrightarrow\frac{2x+1-5x-1}{4}=0\)

\(\Leftrightarrow\frac{-3x}{4}=0\)

\(\Rightarrow-3x=0\)

\(\Rightarrow x=0\)

e)

\(\frac{3\cdot\left(5x-2\right)}{4}-2=\frac{7x}{3}-5\cdot\left(x-7\right)\)

\(\Leftrightarrow\frac{45x-18-24-28x+60x-420}{12}=0\)

\(\Leftrightarrow\frac{77x-462}{12}=0\)

\(\Rightarrow77x-462=0\)

\(\Rightarrow x=\frac{462}{77}=6\)

\(\frac{3x-7}{5}=\frac{2x-1}{3}\)

\(\Leftrightarrow9x-21=10x-5\)

\(\Leftrightarrow-x=16\Leftrightarrow x=-16\)

\(\frac{4x-7}{12}-x=\frac{3x}{8}\)

\(\Leftrightarrow\frac{4x-7-12x}{12}=\frac{3x}{8}\)

\(\Leftrightarrow\frac{-7-8x}{12}=\frac{3x}{8}\)

\(\Leftrightarrow-56-64x=36x\)

\(\Leftrightarrow-56=100x\Leftrightarrow x=\frac{-14}{25}\)

\(\frac{x-2009}{1234}+\frac{x-2009}{5678}-\frac{x-2009}{197}=0\)

\(\Leftrightarrow\left(x-2019\right)\left(\frac{1}{1234}+\frac{1}{5678}-\frac{1}{197}\right)=0\)

Vì \(\left(\frac{1}{1234}+\frac{1}{5678}-\frac{1}{197}\right)\ne0\)nên x - 2019 = 0

Vậy x = 2019

\(\frac{5x-8}{3}=\frac{1-3x}{2}\)

\(\Leftrightarrow10x-16=3-9x\)

\(\Leftrightarrow19x=19\Leftrightarrow x=1\)

\(\frac{x-5}{6}-\frac{x-9}{4}=\frac{5x-3}{8}+2\)

\(\Rightarrow\frac{4x-20-6x+54}{24}=\frac{5x-3+16}{8}\)

\(\Rightarrow\frac{-2x+34}{24}=\frac{5x+13}{8}\)

\(\Rightarrow-16x-272=120x+312\)

\(\Leftrightarrow-136x=584\Leftrightarrow x=\frac{-73}{17}\)

Đây là những bài cơ bản mà bạn!

\(\frac{5x-2}{3}=\frac{5-3x}{2}\)

\(< =>\frac{\left(5x-2\right).2}{6}=\frac{\left(5-3x\right).3}{6}\)

\(< =>\left(5x-2\right).2=\left(5-3x\right).3\)

\(< =>10x-4=15-9x\)

\(< =>10x+9x=15+4\)

\(< =>19x=19< =>x=1\)

\(\frac{10x+3}{12}=1+\frac{6+8x}{9}\)

\(< =>\frac{\left(10x+3\right).3}{36}=\frac{36}{36}+\frac{\left(6+8x\right).4}{36}\)

\(< =>\left(10x+3\right).3=36+\left(6+8x\right).4\)

\(< =>30x+9=36+24+32x\)

\(< =>32x-30x=9-36-24\)

\(< =>2x=9-60=-51< =>x=-\frac{51}{2}\)

Các ĐKXĐ: bạn tự tìm

a)

\(\frac{11x+10}{3x-3}+\frac{15x+13}{4-4x}=\frac{11x+10}{3(x-1)}-\frac{15x+13}{4(x-1)}=\frac{4(11x+10)-3(15x+13)}{12(x-1)}\)

\(=\frac{-x+1}{12(x-1)}=\frac{-(x-1)}{12(x-1)}=\frac{-1}{12}\)

b)

\(\frac{5x+3}{x^2-3x}+\frac{9-x}{9-3x}=\frac{5x+3}{x(x-3)}+\frac{x-9}{3x-9}=\frac{5x+3}{x(x-3)}+\frac{x-9}{3(x-3)}\)

\(=\frac{3(5x+3)}{3x(x-3)}+\frac{x(x-9)}{3x(x-3)}=\frac{x^2+6x+9}{3x(x-3)}=\frac{(x+3)^2}{3x(x-3)}\)

c)

\(\frac{4xy-1}{5x^2y}-\frac{2xy-1}{5x^2y}=\frac{(4xy-1)-(2xy-1)}{5x^2y}=\frac{2xy}{5x^2y}=\frac{2}{5x}\)

d)

$\frac{x+8}{x^2-16}-\frac{2}{x^2+4x}=\frac{x+8}{(x-4)(x+4)}-\frac{2}{x(x+4)}$

$=\frac{x(x+8)}{x(x-4)(x+4)}-\frac{2(x-4)}{x(x+4)(x-4)}$

$=\frac{x^2+8x-2(x-4)}{x(x+4)(x-4)}=\frac{x^2+6x+8}{x(x+4)(x-4)}$

$=\frac{(x+2)(x+4)}{x(x+4)(x-4)}=\frac{x+2}{x(x-4)}$
e)

$\frac{x^2-49}{2x+1}.\frac{3}{7-x}=\frac{(x-7)(x+7)}{2x+1}.\frac{-3}{x-7}$

$=\frac{-3(x+7)}{2x+1}$

f)

$\frac{3x^2-2x}{x^2-1}.\frac{1-x^4}{(2-3x)^3}$

$=\frac{2x-3x^2}{x^2-1}.\frac{x^4-1}{(2-3x)^3}=\frac{x(2-3x)(x^2-1)(x^2+1)}{(x^2-1)(2-3x)^3}$

$=\frac{x(x^2+1)}{(2-3x)^2}$
g)

$\frac{5xy}{2x-3}:\frac{15xy^3}{12-8x}=\frac{5xy}{2x-3}.\frac{12-8x}{15xy^3}$

$=\frac{5xy}{2x-3}.\frac{-4(2x-3)}{15xy^3}=\frac{-4}{3y^2}$

h)

$\frac{x^2+2x}{3x^2-6x+3}:\frac{2x+4}{5x-5}=\frac{x(x+2)}{3(x-1)^2}:\frac{2(x+2)}{5(x-1)}$

$=\frac{x(x+2)}{3(x-1)^2}.\frac{5(x-1)}{2(x+2)}$

$=\frac{5x}{6(x-1)}$

a/ \(7x-5=13-5x\)

\(\Leftrightarrow7x+5x=13+5\)

\(\Leftrightarrow12x=18\)

\(\Leftrightarrow x=\frac{3}{2}\)

b/\(5\left(2x-3\right)-4\left(5x-7\right)=19-2\left(x+11\right)\)

\(\Leftrightarrow10x-15-20x+28=19-2x-22\)

\(\Leftrightarrow10x-20x+2x=19-22-28+15\)

\(\Leftrightarrow-8x=-16\)

\(\Leftrightarrow x=2\)

c/ \(\frac{2x-1}{3}-\frac{5x+2}{7}=x+13\)

\(\Leftrightarrow\frac{7\left(2x-1\right)-3\left(5x+2\right)-21\left(x+13\right)}{21}=0\)

\(\Leftrightarrow14x-7-15x-6-21x-273=0\)

\(\Leftrightarrow-22x-286=0\)

\(\Leftrightarrow x=-13\)

e/ \(\frac{2}{x+1}-\frac{1}{x-2}=\frac{3x-11}{\left(x+1\right)\left(x+2\right)}\)

\(\Leftrightarrow\frac{2}{x+1}-\frac{1}{x-2}-\frac{3x-11}{\left(x+1\right)\left(x+2\right)}=0\)

\(\Leftrightarrow\frac{2\left(x-2\right)\left(x+2\right)-\left(x+1\right)\left(x+2\right)-\left(3x-11\right)\left(x-2\right)}{\left(x+1\right)\left(x-2\right)\left(x+2\right)}=0\)

\(\Leftrightarrow\frac{2\left(x^2-4\right)-\left(x^2+3x+2\right)-\left(3x^2-17x+22\right)}{\left(x+1\right)\left(x-2\right)\left(x+2\right)}=0\)

\(\Leftrightarrow2x^2-8-x^2-3x-2-3x^2+17x-22=0\)

\(\Leftrightarrow-2x^2+14x-32=0\)

\(\Leftrightarrow x^2-7x+16=0\)

\(\Leftrightarrow x=\frac{-\left(-7\right)\pm\sqrt{\left(-7\right)^2-4.1.16}}{2}\)

\(\Leftrightarrow x=\frac{7\pm\sqrt{-15}}{2}\left(ktm\right)\)

\(\Leftrightarrow x\in\varnothing\)

Bài 1:

a) \(7x-5=13-5x\)

\(\Leftrightarrow7x+5x=13+5\)

\(\Leftrightarrow12x=18\)

\(\Leftrightarrow x=18:12\)

\(\Leftrightarrow x=\frac{3}{2}.\)

Vậy phương trình có tập hợp nghiệm là: \(S=\left\{\frac{3}{2}\right\}.\)

b) \(5.\left(2x-3\right)-4.\left(5x-7\right)=19-2.\left(x+11\right)\)

\(\Leftrightarrow10x-15-\left(20x-28\right)=19-\left(2x+22\right)\)

\(\Leftrightarrow10x-15-20x+28=19-2x-22\)

\(\Leftrightarrow13-10x=-3-2x\)

\(\Leftrightarrow13+3=-2x+10x\)

\(\Leftrightarrow16=8x\)

\(\Leftrightarrow x=16:8\)

\(\Leftrightarrow x=2.\)

Vậy phương trình có tập hợp nghiệm là: \(S=\left\{2\right\}.\)

c) \(\frac{2x-1}{3}-\frac{5x+2}{7}=x+13\)

\(\Leftrightarrow\frac{7.\left(2x-1\right)}{7.3}-\frac{3.\left(5x+2\right)}{3.7}=\frac{21.\left(x+13\right)}{21}\)

\(\Leftrightarrow\frac{14x-7}{21}-\frac{15x+6}{21}=\frac{21x+273}{21}\)

\(\Leftrightarrow14x-7-\left(15x+6\right)=21x+273\)

\(\Leftrightarrow14x-7-15x-6=21x+273\)

\(\Leftrightarrow-x-13=21x+273\)

\(\Leftrightarrow-x-21x=273+13\)

\(\Leftrightarrow-22x=286\)

\(\Leftrightarrow x=286:\left(-22\right)\)

\(\Leftrightarrow x=-13.\)

Vậy phương trình có tập hợp nghiệm là: \(S=\left\{-13\right\}.\)

Chúc bạn học tốt!