## Changing the Subject of a Simple Rational Algebraic Fraction

\[x\]

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

\[x, \: 4x-2\]

.\[x=\frac{-5y+3}{4x-2}\]

.