could anyone please help me with this question
express the function f(x)=6x-5/3x+1 in the form a+(b/(x+c)
the answer is f(x)= 2-(7)/(3x+1)
thanks
Hello, kaz93!
Chris showed you a clever method.
$\displaystyle \text{Express the function }f(x)\:=\:\dfrac{6x-5}{3x+1}\,\text{ in the form: }\:a+\dfrac{b}{x+c}$
We can use old-fashioned Long Division.
. . $\displaystyle \begin{array}{ccccc}
&&&& 2 \\
& & -- & -- & -- \\
3x+1 & \bigg) & 6x & - & 5 \\
& & 6x & + & 2 \\
& & -- & -- & -- \\
&&& - & 7 \end{array}$
$\displaystyle \text{Therefore: }\;\;\dfrac{6x-5}{3x+1} \;\;=\;\;2 - \dfrac{7}{3x+1}$