Part A: Term [tex]5ac[/tex] is used to bring denominator of [tex]35a^{3} c^{3}[/tex]
Part B: Term [tex]a+4[/tex] is used to bring denominator of [tex]16-a^{2}[/tex]
Explanation:
Part A: To bring the fraction [tex]\frac{b}{7a^{2}c }[/tex] to a denominator of [tex]35a^{3} c^{3}[/tex], we need to multiply the denominator by the term [tex]5ac[/tex]
The term [tex]5ac[/tex] is determined by [tex]\frac{35a^{3} c^{3}}{7a^{2}c }}[/tex] which equals [tex]5ac[/tex]
Thus, the fraction becomes
[tex]\frac{b}{7a^{2}c }\times\frac{5ac}{5ac} =\frac{5abc}{35a^{3} c^{3}}[/tex]
Thus, the term [tex]5ac[/tex] is used to bring denominator of [tex]35a^{3} c^{3}[/tex]
Part B: To bring the fraction [tex]\frac{a}{a-4}[/tex] to a denominator of [tex]16-a^{2}[/tex], we need to multiply the denominator by [tex]a+4[/tex]
Thus, we have,
[tex]\frac{a}{a-4}\times\frac{a+4}{a+4} =\frac{a(a+4)}{16-a^{2}}[/tex]
Thus, the term [tex]a+4[/tex] is used to bring denominator of [tex]16-a^{2}[/tex]
