Question

Add:$\frac{4}{\mathrm{m}+3}+\frac{3}{\mathrm{m}+4}$.

Short answer

The addition of rational expression is$\frac{7m+25}{\left(m+3\right)\left(m+4\right)}$

Step-by-step solution

Given information 

The given rational expression is$\frac{4}{\mathrm{m}+3}+\frac{3}{\mathrm{m}+4}$.

Simplification of the rational expression 

The LCD of $\left(\mathrm{m}+4\right)\left(\mathrm{m}+3\right)$.

Change into equivalent rational expressions with LCD $\left(\mathrm{m}+4\right)\left(\mathrm{m}+3\right)$.

$$\begin{gathered} =\frac{4\times \left(\mathrm{m}+4\right)}{\left(\mathrm{m}+4\right)\left(\mathrm{m}+3\right)}+\frac{3\times \left(\mathrm{m}+3\right)}{\left(\mathrm{m}+3\right)\left(\mathrm{m}+4\right)} \\ =\frac{4\mathrm{m}+16}{\left(m+4\right)\left(m+3\right)}+\frac{3m+9}{\left(m+4\right)\left(m+3\right)} \\ =\frac{4m+3m+16+9}{\left(m+4\right)\left(m+3\right)} \\ =\frac{7m+25}{\left(m+4\right)\left(m+3\right)} \end{gathered}$$