Question

I don’t know how to solve rational expressions please help!

Answer 1

`\text{First we need to factorise the numerator and denominator of the fraction.}\\\text{We will do it using a product-sum method.}\\\text{First of all, take the numerator:}\\g^2+7g+12\\\text{Here, think of two numbers whose sum is 7 and product is 12. They are 4 and}\\\text{3.}\\\text{Now we write 7 as (3+4).}\\g^2+(4+3)g+12\\=g^2+4g+3g+12\\=g(g+4)+3(g+4)\\=(g+4)(g+3)`

`\text{Then we proceed to factorise denominator as follows:}\\g^2-2g-24\\\text{In case of negative constant, we need to think of two numbers whose difference}\\\text{is middle term, i.e. 2 and the product is constant i.e. 24.}\\\text{These two numbers are 6 and 4.}\\\text{Now we write 2 as }(6-4).\\g^2-(6-4)g-24\\=g^2-6g+4g-24\\=g(g-6)+4(g-6)\\=(g-6)(g+4)`

`\text{Now,}\\(g^2+7g+12)/(g^2-2g-24)=((g+4)(g+3))/((g-6)(g+4))=(g+3)/(g-6)`