\[\text{Question 1}\\\text{Express the expresion as a single fraction}\\\frac{1}{x-1}-\frac{2}{x+3}\\[30pt]\text{Question 2}\\\text{Simplify the expression}\\\frac{6-x-x^{2}}{x^{2}-4}\\[30pt]\text{Question 3}\\\text{Simplify the expression}\\\frac{x+1}{(x+1)^{2}}\\[30pt]\text{Question 4}\\\text{Simplify the expression}\\\frac{p-1}{1-\frac{1}{p}}\\[30pt]\text{Question 5}\\\text{Simplify the expression}\\\frac{a}{a^{2}+a}\\[30pt]\text{Question 6}\\\text{Simplify the expression}\\\frac{(x+1)^{2}}{x^{2}-1}\\[30pt]\text{Question 7}\\\text{Simplify the expression}\\\frac{x^{2}+6x+5}{x^{2}+8x+7}\\[30pt]\text{Question 8}\\\text{Find the value of x for which expression}\\\frac{9}{x}-\frac{b}{x^{2}+6x-7}\\[15pt]\text{is not defined}\\[30pt]\text{Question 8}\\\text{Expand and simplify the expression}\\\frac{1}{5}(10c+2d)+\frac{1}{3}(4c-d)\\[30pt]\text{Question 9}\\\text{Simplify the expression}\\\frac{\frac{1}{a}+1}{a+1}\\[30pt]\text{Question 10}\\\text{Factorise}\\\ w^{4}-81z^{2}\]
\[\text{Find how to solve tricky algebra with step by step guides |#SAT AND GSCE PASCO}\\[35pt]\text{If}\quad (3.46)^{2}-(1.54)^{2}=10x,\quad\text{find the value of x}\\[10pt]\text{Solution}\\[10pt]\text{Given}\quad(3.46)^{2}-(1.54)^{2}=10x\\[10pt]\text{Step .1}\qquad\text{Since there is two perfect squares, we take difference of two squares}\\[10pt]\text{Examples;}\quad a^{2}-b^{2}=(a-b)(a+b)\\[10pt]\Rightarrow\qquad(3.46-1.54)(3.46+1.54)=10x\\[10pt]\text{Step.2}\qquad\text{Simplify}\\[10pt]\Rightarrow\qquad(1.92)(5)=10x\\[10pt]\Rightarrow\qquad 9.6=10x\\[10pt]\text{Step 3.}\qquad\text{Divide both terms by 10 to make x stands alone}\\[10pt]\Rightarrow\qquad\frac{10x}{10}=\frac{9.6}{10}\\[10pt]\Rightarrow\qquad x=\frac{9.6}{10}\\[10pt] \therefore\qquad x=0.96\]
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