\(\dfrac{2x+1}{3}=\dfrac{x-5}{2}\\ \Leftrightarrow2\left(2x+1\right)=3\left(x-5\right)\\ \Leftrightarrow4x+2=3x-15\\ \Leftrightarrow4x+2-\left(3x-15\right)=0\\ \Leftrightarrow4x-3x+2+15=0\\ \Leftrightarrow x+17=0\\ \Leftrightarrow x=-17\)

\(a,\\ x:144-23=121\\ x:144=121+23\\ x:144=144\\ x=144:144\\ x=1\\ b,\\ \left(2x+1\right)\cdot2907=8721\\ 2x+1=8721:2907\\ 2x+1=3\\ 2x=3-1\\ 2x=2\\ x=2:2\\ x=1\\ c,\\ \left(4x-16\right):1905=60\\ 4x-16=60\cdot1905\\ 4x-16=114300\\ 4x=114300+16\\ 4x=114316\\ x=114316:4\\ x=28579\)

\(M=1+\left(\dfrac{2a+\sqrt{a}-1}{1-a}-\dfrac{2a\sqrt{a}-\sqrt{a}+1}{1-a\sqrt{a}}\right)\left(\dfrac{a-\sqrt{a}}{2\sqrt{a}-1}\right)\\ =1+\left(\dfrac{\left(\sqrt{a}-1\right)^2}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)}-\dfrac{\sqrt{a}\left(1+\sqrt{a}+a\right)}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}+a\right)}\right)\cdot\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{2\sqrt{a}-1}\\ =1+\left(\dfrac{\left(1-\sqrt{a}\right)^2}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)}-\dfrac{\sqrt{a}}{\left(1-\sqrt{a}\right)}\right)\cdot\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{2\sqrt{a}-1}\\ =1+\left(\dfrac{1-\sqrt{a}}{1+\sqrt{a}}-\dfrac{\sqrt{a}}{1-\sqrt{a}}\right)\cdot\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{2\sqrt{a}-1}\\ =1+\left(\dfrac{\left(1-\sqrt{a}\right)^2}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)}-\dfrac{\sqrt{a}\left(1+\sqrt{a}\right)}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)}\right)\cdot\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{2\sqrt{a}-1}\\ =1+\dfrac{1-2\sqrt{a}+a-\sqrt{a}-a}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)}\cdot\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{2\sqrt{a}-1}\\ =1+\dfrac{\sqrt{a}}{1+\sqrt{a}}=\dfrac{1+2\sqrt{a}}{1+\sqrt{a}}\)

\(2^{17-x}=\left(2^3\right)^4\cdot4^2\\ 2^{17-x}=2^{12}\cdot4^2\\ 2^{17-x}=2^{12}\cdot\left(2^2\right)^2\\ 2^{17-x}=2^{12}\cdot2^4\\ 2^{17-x}=2^{16}\\ \Rightarrow17-x=16\\ x=17-16\\ x=1\)

\(112\cdot\left(-63\right)+63\cdot\left(-53\right)-63\cdot26\\ =\left(-112\right)\cdot63+63\cdot\left(-53\right)-63\cdot26\\ =63\cdot\left[\left(-112\right)+\left(-53\right)-26\right]\\ =63\cdot\left(-191\right)\\ =-12033\)

gan ghê :) 

còn cop luôn cả latex nè