\[x\]
the subject of the formula \[y=\frac{2x+3}{4x+5}\]
Start by clearing the fraction (multiplying by
\[4x+5\]
).\[y(4x+5)=2x+3\]
\[4xy+5y=2x+3\]
We are to make
\[x\]
the subject so need to move all the terms containing \[x\]
to the same side of the equals sign, and all other terms to the other side.\[4xy-2x=-5y+3\]
Now factorise with
\[x\]
\[x(4x-2)=-5y+3\]
Finally divide by the coefficient of
\[x, \: 4x-2\]
.\[x=\frac{-5y+3}{4x-2}\]
.