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vaieri [72.5K]
3 years ago
11

Step-by-step solution to:

D%7B4x%20-%203%7D%20" id="TexFormula1" title=" - \frac{3}{4x - 7} = \frac{x}{4x - 3} " alt=" - \frac{3}{4x - 7} = \frac{x}{4x - 3} " align="absmiddle" class="latex-formula">
Mathematics
1 answer:
stealth61 [152]3 years ago
5 0
The key to solving this problem is recognizing it is a proportion and can be solved using the technique called cross-multiplication. This m<span>eans that you are multiplying the numerator of each side by the denominator of the other side.</span>

\frac{-3}{4x-7} =  \frac{x}{4x-3}

You multiply the numerator of the first side by the denominator of the second and the denominator of the first by the numerator of the second.

-3(4x-3)=x(4x-7)

Simplify.

-12x+9=4x^2-7x

4x^2+5x-9=0

Factor.
4x^2-4x+9x-9=0 \\ 4x(x-1)+9(x-1)=0 \\ (4x+9)(x-1)=0

Set each factor equal to zero and solve for x.

4x+9=0 \\ x=-9/4

x-1=0 \\ x=1

Finally, you want to look at the original expression and make sure that these solutions don't violate any restrictions on division by zero.

For the right side, we see that 4x-7 ≠ 0, so x ≠ 7/4. For the left side, we see that 4x-3 ≠ 0, so x <span>≠ </span>3/4. This means our solutions are valid.

x = -9/4, x = 1

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