\binom{4a + 3}{5} - \binom{2a + 3}{3} simplify the fraction ​

Question

`\binom{4a + 3}{5} - \binom{2a + 3}{3}`
simplify the fraction
​

Answer 1

I assume your question was to simplify the following fraction ;

`{:\implies \quad \sf (4a+3)/(5)-(2a+3)/(3)}`

Taking LCM will yield ;

`{:\implies \quad \sf (3(4a+3)-5(2a+3))/(15)}`

`{:\implies \quad \sf (12a+9-10a-15)/(15)}`

`{:\implies \quad \boxed{\bf (2a-6)/(15)}}`

This is the required answer