Show that if `f: R-{7/5}->R-{3/5}`is defined by `f(x)=(3x+4)/(5x-7)`and `g: R-{3/5}->R-{7/5}`is define by `g(x)=(7x+4)/(5x-3)`, then `fog=I_A`and `gof=I_B`, where `A=R-{3/5}, B=R-{7/5}; I_A(x)=x ,AAx in A , I_B(x)=x ,AAx in B` are called ideal

Explanation

To show that \( f \circ g = I_A \) and \( g \circ f = I_B \), where \( f(x) = \frac{3x + 4}{5x - 7} \) and \( g(x) = \frac{7x + 4}{5x - 3} \), we will compute both compositions step by step.

### Step 1: Compute \( g(f(x)) \)

1. **Substitute \( f(x) \) into \( g(x) \)**:
\[ g(f(x)) = g\left(\frac{3x + 4}{5x - 7}\right) = \frac{7\left(\frac{3x + 4}{5x - 7}\right) + 4}{5\left(\frac{3x + 4}{5x - 7}\right) - 3} \]
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